# User talk:Cuzkatzimhut

 The Original Barnstar Inspiring brilliance Dick Chu (talk) 13:06, 24 December 2009 (UTC)
 The Working Man's Barnstar Truly great work
 The E=mc² Barnstar Einstein would admire you Dick Chu (talk) 13:06, 24 December 2009 (UTC)
 The Tireless Contributor Barnstar We appreciate your effort Dick Chu (talk) 13:06, 24 December 2009 (UTC)
 The Resilient Barnstar Your efforts motivate us Dick Chu (talk) 13:06, 24 December 2009 (UTC)
 The Socratic Barnstar Zohanmesser (talk) 19:57, 7 April 2009 (UTC)
 The E=mc² Barnstar Zohanmesser (talk) 19:57, 7 April 2009 (UTC)
 The Editor's Barnstar Zohanmesser (talk) 19:57, 7 April 2009 (UTC)

 The Tireless Contributor Barnstar Dear Cuzkatzimhut, please accept this barnstar in recognition of making over 1,000 edits to articles on English Wikipedia, and for your amazing contributions to math and science related content. Thank you so much for all your hard work! Maryana (WMF) (talk) 21:36, 10 April 2012 (UTC)

 The Biography Barnstar For all the effort you put into fixing factual and translation errors, and making the article better overall. Splendid work! M∧Ŝc2ħεИτlk 16:51, 28 October 2013 (UTC)

 The Writer's Barnstar Good idea with this edit: Exponential of a Pauli vector Brent Perreault (talk) 18:55, 2 November 2013 (UTC)

## Perturbation methods

Dear Cuzkatzimhut, I'm very sorry for some mistakes in the page Perturbation theory but I think the original purpose is rather correct: I wish to specify that these ones are applications of analytical perturbation methods to QM, while many other fields have seen perturbation methods like neutronics basing on linear Boltzmann equation, viscoelasticity and so on. That is also the reason I have just suggested in the discussion of [Mathematical] Perturbation Theory page to solve the ambiguity on one hand by inverting the redirect with perturbation methods, and on the other hand to rename the Perturbation Theory (QM) page into Quantum perturbation Theories, (since there are more than one). Please let me know what do you think about my suggestion! 95.238.49.157 (talk) 18:11, 7 October 2014 (UTC)

It would be best if you got a WP instead of revealing your IP and subverting your purposes. I think it is a bit ambitious to change universally accepted terms, as per textbook and paper usage, starting from wikipedia, the first resort of a user. And completely unhelpful to efface the primary conceptual idea behind the methods in the opening paragraph. A reader looking for "stationary perturbation theory" will be hard-pressed looking for the relevant section, and hitting the eponymized term, R-S, you introduced. Eponymy is strongly deprecated in WP, as an indirect path to writing history, and can generate obvious tensions. In any case, I could not imagine anyone getting confused by the straw-man notional ambiguities you seem to be inventing, and so my own interest in the matter is terminated; but I have the sense the 82 page watchers might take issue with your edits, especially as you did not discuss them in the article's talk page first. Cuzkatzimhut (talk) 18:25, 7 October 2014 (UTC)
I must say first thank you for your positive politeness, I especially liked the pyrotechnic assembly "straw-man notional ambiguities": this rather seems to me an example of straw-man argument. A reader looking for "stationary perturbation theory" is not really a freshman so maybe he already knows something like the universally accepted names since at least 50 years (for example in perturbation chapter of Butkov, Mathematical physics you can see Rayleigh-Schroedinger also in the names of paragraphs: so why don't we change name to the Schroedinger equation?). Thank you also for the intimidating conclusion, it was so necessary: now these 82 page watchers are really scaring the shit out of me... 95.238.49.157 (talk) 09:11, 8 October 2014 (UTC)

## Baker–Campbell–Hausdorff formula

Hi Cuzkatzimhut! I see you have been working on the BCH article. I have a couple of questions, and you might be the one to ask? I have made a few small additions (let me know if they are bad). One addition is a note box on convergence, I placed it at the first appropriate place I could see. It turned out to be the "existence" section. But as I read it more carefully, it seems that convergence is not an issue there at all. Is this guess correct?

Another thing, when I rewrote classical group, there was an addition by you that got lost. I couldn't at that moment find a place for it in the new version because I din't understand it. I meant to ask you about how to fit it in, but I forgot all about it. Do you remember what it was? Something with Moyal algebra? YohanN7 (talk) 22:15, 12 October 2014 (UTC)

Sorry I won't be helpful with the first question... The improvements look fine--even though Dirac's creation and annihilation algebra was useful long before QFT considerations emerged...Weyl's and von Neumann's work on the Heisenberg group got going in 1927, and 1930, if I recall, and they certainly relied on the degenerate baby BCH. I will keep mum on issues of convergence, as I always find workarounds for such things at the boundaries of convergence, and I fit them to circumstances... You might see Logarithm of a matrix? I cannot see a trivial nonsingular example illustrating trouble, though, i.e. well-defined exp(X) exp(Y) incapable of being expressed as exp of some Z... In fact, the QM applications deal with unbounded operators, x, ∂, etc... Weyl appreciated exponential operators such as the translation operator, exp(∂), are better behaved than ∂. It might be useful for your footnote if you found a sweet counterexample...
The sentence you deleted in March can be found by clicking on any prior version of classical group... it was "All classical Lie algebras may be fit into infinite dimensional Lie algebras, such as the Moyal algebra." The ref by Fairlie et al it had describes how all series An, Bn, Cn, and Dn, for any n can fit quite elegantly into Moyal, "the mother of all Lie algebras", and so then also the exceptionals, since they fit into these 4 series themselves. It is an aside, so I have no clue where it might belong... ideally in Lie algebra#Classification, but it was missing from there, and back-linked instead to classical groups--- which these series of Lie algebras generated... I'm not sure what is to be done now, beyond the obvious, which I don't have the time to do myself, namely defining "classical Lie algebras" in Lie algebra itself. Best, Cuzkatzimhut (talk) 00:32, 13 October 2014 (UTC)
Ah, yes, how could I have forgotten e.g Dirac's treatment of the Harmonic oscillator, etc. They created/destroyed quanta of sorts (phonons?), not particles so not QFT. How about renaming the section to Quantum mechanics and quantum field theory?
About convergence: I don't have any technical problems with it. I was mostly curious. The thing is that in the construction given in the section one deals with "formal power series", and one such that is divergent for given X and Y is still a formal power series. I think for the proof in that section, perhaps convergence issues are immaterial. Then again, perhaps not. That needs a note box of its own, and I'll could move the present one to an appropriate place. But I am uncertain. The way the intro is formulated does give the idea that the formula will hold for all X and Y. The proof, on the other hand, seems to promise that any BCH formula will either give the right answer, or the wrong answer (because X and Y are too large) but still in the Lie algebra, or diverge to infinity. Do you now understand my problem with it?
The Moyal algebra: It could surely go into Classical group. But I think it needs to be worked on. Classical group is now a rather "explanatory" article, and the statement, as it stands, is "too difficult". You would go from junior undergrad level to beginning PhD level. It needs to be fleshed out on, I'd be happy to do it, but I can't right now. I'd need to read up.
I'll have a look at perturbation theory (quantum mechanics) tomorrow evening. It's really past bedtime. YohanN7 (talk) 02:00, 13 October 2014 (UTC)
Right, as you put it, footnotes in both cases could address the Graduate student level subtleties. All your proposals appear salutary. As said, a toy example of validity beyond the radius of convergence might be interesting... I mostly work with examples I understand, and have never run into problems using the unbounded operators x and d/dx, etc.. in these formulas... in fact that's when they prove most useful. Cuzkatzimhut (talk) 11:09, 13 October 2014 (UTC)
Come to think of it, the toy example would be the easiest thing in the world for me to produce. I have written a private little math library, and this includes matrices, including exp and log. Believe me, the radius of convergence is there for the log-series. By the way, I have reverted everything the IP (above) have produced (like 5 articles). He is not here to cooperate. I left one article about a Mexican power plant. He is obviously vandalizing there too, but it is nothing I can prove. Can you have a look? If he goes on it's time to call in an admin. YohanN7 (talk) 12:45, 13 October 2014 (UTC)

──────────────────────────────────────────────────────────────────────────────────────────────────── Yes, such an example would probably help! (If you were ambitious, you might also finesse Stone–von Neumann theorem which utilizes BCH, essentially for â and â.) The Bologna IP might well be used by more than one person. The Laguna Verde edits, however, might not be inappropriate, since the upscaling of power units by 3 orders of magnitude seems to be bringing that plant up to standard power generation rates of nuclear plants in general. But what do I know... Cuzkatzimhut (talk) 19:21, 13 October 2014 (UTC)

Hi. I checked over at Stone–von Neumann theorem. It seems ok. They use
${\displaystyle [[P,Q]P]=[[P,Q]Q]=0}$
then
${\displaystyle e^{P}e^{Q}=e^{P+Q+{\frac {1}{2}}[P,Q]},}$
the chopped off infinite bracket series. It can be proved without BCH. The problem is probably not with such identities (even with more terms on the right). The problems come when you say
${\displaystyle Z=\mathrm {log} (e^{X}e^{Y})=X+Y+{\frac {1}{2}}[X,Y]\cdots ,}$
because then X and Y must be small. Both books (Brian C. Hall + Wulf Rossmann) I have that cover this point this out, and quote the numbers:
${\displaystyle \mathrm {log} (\mathrm {exp} (A))=A{\text{ if }}||A||<\mathrm {log} 2,\quad \mathrm {exp} (\mathrm {log} A)=A{\text{ if }}||A||<1.}$
I think begin to see this a bit clearer now. YohanN7 (talk) 06:51, 14 October 2014 (UTC)
Well, one might always multiply A with a parameter s small enough to satisfy such inequalities, and ask whether the answer itself has broader validity for more general s than the actual method of calculation warranted. In practice, one hardly cares what the series does--one uses it as a crutch just to get to a closed compact expression, so all these questions of convergence are left for final cleanups. The caveat is fine, but, as in the case of generalized functions, a stout man's heart breaks bad luck... Cuzkatzimhut (talk) 10:54, 14 October 2014 (UTC)
The original problem eZ = eXeY isn't exactly linear. I agree of course. But I'm sure you agree too that an equation with a known domain of validity is incomplete without that domain of validity? You want this info before you decide how bypass it. There are other problems too. If you interpret X, Y and Z as coordinate points in a Lie algebra (exponential coordinates) of elements in the Lie group, the even if BCH in exponentiated form holds mathematically as identities in X, Y and Z, all big, these quantities are no longer coordinate points for group element. In group theory BCH is in general local.
But this brings us back to my original question. Where should this info be put? Where it presently is may be misleading. YohanN7 (talk) 16:24, 14 October 2014 (UTC)
Well, in full agreement, as usual, I'd argue it belongs very near the end, as a "fussing section", like Domain of validity. It would be useful, but, only as a caveat discussion... It would be counterproductive to send somebody away from applying the formula and its algorithmic methods before they have tried something and hit upon a problem. It is best for them to damn the torpedoes, and read up on mathematical subtleties if one came close. It is all stylistic, of course... In my own experience, I have watched people bug eye when I bring them a fish right after their suave proof of the nonexistence of fish... Cuzkatzimhut (talk) 16:38, 14 October 2014 (UTC)
I have just edited (before I saw your comment). The first nb (and the formulation just before it) is changed. I added the full thing to the matrix Lie group section (as an nb besides the equation) where it is decidedly true. YohanN7 (talk) 17:07, 14 October 2014 (UTC)
Would you perhaps say that the formula in question might still be true even if the conditions aren't met? There are certainly parts of matrix space (has to do with eigenvalues) where it would be true for arbitrarily large matrices (would be overkill to put that in). One might argue that only the means of deriving the formula fails. But I'd argue against having a philosophy of "Every formula is true until proven wrong." That would be too optimistic in my taste YohanN7 (talk) 19:12, 14 October 2014 (UTC)

────────────────────────────────────────────────────────────────────────────────────────────────────I suspect it is not worth fussing things too much. I gather we have a problem of language: What most physicists have in mind, once they hear BCH, is most certainly not Dynkin's infinite expansion, but, usually something compact like the ψ expression of section 2.1 (Magnus, Miller, etc...), whatever method one employs in evaluating it (admittedly, often series expansions). Very often, they cut corners, without losing track of the controlling essence of the problem, and take logical leaps harder to justify than to explain, on the way to a correct answer, then proven and justified in several ways. The fact is that many of these expressions are solutions to operator differential equations, and series and combinatorics need never enter, for some applications. So, typically, a derivative operator d/dx may easily be plugged into these expressions, act on fancy functions f(x), and lead to correct results, regardless of presumed intermediate steps failing or not, and fussbudgets in the audience agonizing over square integrability of the relevant expressions or not. But we are talking about hypotheticals. If you had a cogent example illustrating the need of caution and the grim consequences of insouciance, why, it would certainly be useful. Cuzkatzimhut (talk) 19:39, 14 October 2014 (UTC)

Since when isn't providing references enough? The BCH article is within the scope of both physics and math. But all right, I'll produce a set of three matrices from which you cannot solve for Z by taking logarithms. YohanN7 (talk) 19:57, 14 October 2014 (UTC)
Well, I suspect the casual reader will not run to the references... He or she is here precisely in avoidance of hitting the books. Yes, if you have an example of a well defined exp(X) and a well defined exp(Y) which, however, multiply to exp(X) exp(Y) not expressible as an exponential of something, that could scare the reader to be more careful. Going back to what most physicists understand by such a formula, they basically understand it as a fussy group multiplication law in the same parameterization... something like this for SU(2). If they can formally sum a series to get there, they'd do it, but, more often than not, they'd seek the full closed answer without the guileful "benefit" of series expansions. Cuzkatzimhut (talk) 20:58, 14 October 2014 (UTC)
An example such that there is no Z in the Lie algebra for which eZ = eXeY for X, Y in the Lie algebra can be found here: (formula S(8)) Representation theory of the Lorentz group#Non-surjectiveness of exponential mapping. (All exponentials lie in the group, which here is SL(2, C)) This is much much much deeper than what we are discussing.
What we have at hand is that if ||A - I|| > 1 for some matrix A, then log(A) is, in general, not defined. The derivation of the formula in the article (matrix section) is based on taking the log of both sides. I can't see why you insist, though I provided references, that the burden of proof that it doesn't hold for large matrices in general lies on me (no worries, I am having fun actually, haven't programmed for a while). It may hold, though its derivation doesn't, but then that should be referenced. I think it would be quite sensational if it did, and ought to be known by now.
I am working on an example from SU(2). I don't know if I can prove that the formula doesn't hold for it, but it is probably easier to prove that (provided true) than that it, in fact, does hold (if that is the case). To be clear, I am talking about the power series expansion in the matrix section. This seems much like analytic continuation. Sure, things exist and are well defined more everywhere, but you can't use the same expression everywhere. YohanN7 (talk) 21:58, 14 October 2014 (UTC)
All is fine and stable: I don't want to appear to be giving you more work! I suspect the proverbial intelligent, well-meaning reader will automatically take care that things computed are well defined, and, as I mumbled early on, if not, try to fix them. Cuzkatzimhut (talk) 22:50, 14 October 2014 (UTC)

──────────────────────────────────────────────────────────────────────────────────────────────────── (EC) Just to make sure we are on the same page: When I say that log(A) doesn't exist, I do not mean that there is no matrix X(whether in the Lie algebra or not) such that eX = A. One could interpret your last post such that you were under the impression that I meant that. Also, the article Logarithm of a matrix (I din't read it until now) puts this a bit loosely, and doesn't even give the formula below. The definition of log is

${\displaystyle \mathrm {log} (A)=\sum _{k=1}^{\infty }{\frac {(-1)^{k-1}}{k}}(A-1)^{k}.}$

It is this formula that enters into the formulas involving BCH. It is, in general, divergent when

${\displaystyle ||A-1||\geq 1,}$

Surely you agree that formulas based on this can't be expected to have general validity, at least not a priori, and not without proof or reference? YohanN7 (talk) 23:35, 14 October 2014 (UTC)

Yes, indeed, I have been strenuously avoiding your metaphorical "page". I understand that, as a series, you may define the log through the mercator series, routinely, and if it works, fine. But my point is that if one can avoid taking the log, by hook or crook, one should at least try. So the starting point Z=log( expX expY) is fine if the log is well defined; but, if not, there is no reason to throw up one's hands, if one can still try to find some plausible Z. A series expansion is only a means of getting to the answer, not the answer itself, nor even the best way to get to it, much of the time. That's why I prefer Magnus's treatment. But I think much of what's on the Wiki page is sound and can rest in peace, by now. Cuzkatzimhut (talk) 00:25, 15 October 2014 (UTC)
Brilliant! Indeed, the formulas value is mostly theoretical, and our article says so. It also warns about convergence problems in one place and provides limits that guarantees convergence in another. In view of what I found on Googling on the net, while eating a delicious late nigh dinner, that is quite appropriate. It seems like the convergence issue is still these days a subject of active research. And yes, Magnus's name appeared. I'd like to get my hands on his books/papers. YohanN7 (talk) 01:07, 15 October 2014 (UTC)
The doi in ref 11?
An aside on your neat example (S8), not a part of our discussion above: The pathology you mention is but a self-evident singularity of the general case, call it “analytic continuation, if you wish: Since [H,X]= 2X, the generic BCH as per section 2.1 is just exp() exp(bX) = exp (aH + 2ab X/(1−exp(−2a)) ), except when it is not defined, as in the case a = iπ , b=−1, a remarkably isolated singular point, when one has the (S8) pathology, exp( iπ Η) exp(− X)= exp(− X) exp( iπΗ) . it is actually less reader-unfriendly if I take b=1 right at the start and −a=iθ and then take the inverse of the above exp(-θ Η) exp(X) to obtain your expression, exp(−X) exp(iθΗ) = exp (iθH + 2iθ X/(1−exp(2)) ), easier to survey perturbatively in θ... Now, why should I, in good faith, prevent anyone from considering the case θ= 3π/2 after this singularity? But this is just conversation with you, of no consequence to the WP article or footnoting... Cuzkatzimhut (talk) 01:26, 15 October 2014 (UTC)
Thank you for explaining this. At the time I wrote around (S8) I had, of course, no idea that there was a connection in this direction. What is happening is that things that aren't supposed to commute actually commute? It is apparent in (S8) but I never noticed it. By your last remark, do you mean this: Things go nicely for 0 ≤ θ < π but blow up at θ = π. This little explosion should not prevent us from pursuing π < θ < 2π. Tell me if I have understood this correctly.
The doi in ref 11 looks interesting. YohanN7 (talk) 18:11, 15 October 2014 (UTC)
Indeed, yes, yes and yes. exp( iπ Η) is proportional to the identity and commutative with everything. But you actually don't need it, as taking the inverse of the first formulation yields the friendlier identity exp(−X) exp(iθΗ) = exp (iθH + 2iθ X/(1−exp(2)) ). And, yes, all holds for 0 ≤ θ < π and is deprived of meaning at θ= π. I have not investigated larger θs, but why shouldn't one do so? Haven't seen any signs of second sheet or anything. For instance, for θ= 3π/2 we have
${\displaystyle e^{{\frac {3\pi i}{2}}(X+H)}=-i(H+X).}$ Cuzkatzimhut (talk) 18:57, 15 October 2014 (UTC)

## TeX in Pauli Matrices article

(Sorry, I'm new here and still learning wikipedian conventions) Why's the TeX problematic? I thought it was much more readable than the makeshift caret-as-a-hat. Twilightrook (talk) 00:40, 16 October 2014 (UTC)

it is a long discussion, here. Depending on missing MathJax implementation, plain text in many, if not most, browsers can look like a ransom letter, with mismatched font sizes, text lines shifted, etc.. Contributors sometimes unjustifiably assume TeX is easier, and use it in a hurry, but the math templates are there for a reason, and TeX is deprecated. If the caret offended your browser (it is almost certainly a font selection issue in your WP preferences) I will format the non-template one. Cuzkatzimhut (talk) 11:00, 16 October 2014 (UTC)

## Full proof (outline)?

Should we go for a (condensed) full proof of BCH (Dynkins formula)? It would take two more regular-sized sections. One for the differential of exp and one for the proof. YohanN7 (talk) 16:53, 16 October 2014 (UTC)

I'm not sure it is a good idea, but if you have the gumption... Any reader intrigued enough by it ought to hit the books, knowing it exists. Personally, I never use Dynkin's formula, as it is very unfriendly: it is basically an algorithm which produces "just so" terms, without illuminating the functional flows involved. I rather prefer the algorithms of section 2.1, and Magnus' or Miller's short and sweet proofs cannot be beat. (They are summarized in the External Source Crib sheet linked.) But they are not provided here for the same reason. As you pointed out, there are two issues involved: one the general principle that the exponent is in the Lie algebra, taken care of by Friedrich's theorem, and two the explicit form of the group composition law involved, for which Dynkin's algorithm is not as efficient as the others. But, then again, neither I nor you are the intended audience, and I am not good at simulating the mind of the reader, so let me not be discouraging there... Cuzkatzimhut (talk) 17:04, 16 October 2014 (UTC)
I am actually neutral myself. The differential of exp (dexp) is missing altogether Wikipedia from what I can see. So, I though about writing that as a standalone article. Then it struck me that, equipped with that, it would be an easy matter (well, due to others it is fairly short and easy to understand) to prove Dynkin's formula, and it could all be done within this article. But, as I said, I'm neutral.
What would you say about dexp only as a section? I don't know if it has any practical use in this direction. It is certainly used in proofs. Or should it go into its own article? YohanN7 (talk) 17:35, 16 October 2014 (UTC)
A yes, Duhamel's formula, the mainstay of all these algorithms. To my taste, it could either belong, without proof, which would be trivial, in a footnote here; but, as your inspired suggestion puts it, better in a separate short stub (of your making!). The reason is that it is used by itself all the time in the Dyson expansion, in perturbation theory in QFT, in lattice gauge theory, etc., so it is a much broader tool than mere BCH.Cuzkatzimhut (talk) 18:39, 16 October 2014 (UTC)
Here:User:YohanN7/Derivative of the exponential map. I just submitted it. Happy editing! YohanN7 (talk) 14:26, 17 October 2014 (UTC)

### History

I found this in a paper "Lie algebra" (almost a complete book) by Shlomo Sternberg that I'm reading right now:

6. The formula is named after three mathematicians, Campbell, Baker, and Hausdorff. But this is a misnomer. Substantially earlier than the works of any of these three, there appeared a paper by Friedrich Schur, “Neue Begruendung der Theorie der endlichen Transformationsgruppen,” Mathematische Annalen 35 (1890), 161-197. Schur writes down, as convergent power series, the composition law for a Lie group in terms of ”canonical coordinates”, i.e., in terms of linear coordinates on the Lie algebra. He writes down recursive relations for the coefficients, obtaining a version of the formulas we will give below. I am indebted to Prof. Schmid for this reference.

It seems well-referenced enough to deserve mention. Still, it isn't present in the typical literature. YohanN7 (talk) 17:59, 16 October 2014 (UTC)

If you wish, why not, as long as it is concise. Indeed, Wilfried Schmid mentions it in his "Poincare and Lie Groups" article, Bull Amer Math Soc, 6 No 2, March 1982, but he also mentions Lie himself thought such hidebound and pedantic... (I downloaded Schur's paper from the Springer site, and I fear I have to agree with Lie: it is so turgid that, even if the result is there, I just don't want to know where...must be near the Bernoulli generator on page 270.) As always, if you were up to it, extra small facts could not hurt. The important facts, however, needed in the history, is that Campbell did all the heavy lifting with commutators early on, and then Poincare. In an imaginary universe, I'd skip Baker who didn't do that much that was original or salutary, and call it the CPH formula... just kidding! But Sternberg has the guts and taste to call it CBH! Cuzkatzimhut (talk) 18:39, 16 October 2014 (UTC)

PS. I see my favorite version in (1.2) of Sternberg's notes (also possibly worth linking in the article?). You might be interested to know that in Varadarajan's book, the formula comes out of lectures by Bargmann he attended at PU. Cuzkatzimhut (talk) 19:07, 16 October 2014 (UTC)

This probably means it's worthwhile to invest in Varadarajan's book. My understanding (the little I have) comes mostly from the matrix Lie group point of view. It's time to go deeper, and Sternberg's paper seems perfect for an introduction to the manifold side of affairs. His equation (1.11) is used (and his paper referenced) in the new article draft. YohanN7 (talk) 14:26, 17 October 2014 (UTC)
Yes, Varadarajan's book is fine, but basically Sternberg's book does the same, and especially Willard Miller's---my own source of wisdom, cf. the Crib notes, etc... Your proposed article looks good. I have not tracked down the attribution to Duhamel, but you may have noticed top-appearing google results calling it that. Perhaps you want to stick in a footnote to the effect that the proof is evident from the definition of the exponential as a large N limit of the monomial, exp(X(t)) = (1+X(t)/N)N; that is, differentiation leads to a sum of N terms, going to an integral, etc... Further, I have been stumbling on your function φ or its multiplicative inverse, ψ, the generating function of Bernoulli numbers, all my life, but have never seen a "name" for it... does it have one? Finally, I suspect Magnus expansion is better than the wikilink to the Dyson series. Cuzkatzimhut (talk) 14:46, 17 October 2014 (UTC)
I did the same thing, i.e. Googeled, found the same thing and was content with that, though a proper reference would be much better. About your baby proof, one needs to assume that X(t) does not commute with its derivative, right? Otherwise the middle factor (with the Φ(-adX) reduces to 1 for me - as it should I guess. It doesn't seem entirely trivial to get to the right expression. YohanN7 (talk) 16:33, 17 October 2014 (UTC)
Yes, of course, it is only when X(t) fails to commute with its derivative when the derivative of the exponential is nontrivial... In that case it would be just the conventional scalar result for commutative quantities! Cuzkatzimhut (talk) 16:38, 17 October 2014 (UTC) All I am saying is, loosely, ∂ (1+X(t)/N)N =∑m=1N (1+X(t)/N)N-m X' (1+X(t)/N)m /N so in the limit ∂ exp(X) = ∫ds exp((1-s)X) X' exp(sX) . The rest is dressing up ... Cuzkatzimhut (talk) 16:46, 17 October 2014 (UTC)
I'm at the middle equation in my sandbox. I was worried that I had to "manually" commute the derivative to the right keeping track of everything. Now I see how the integral relieves me of that. (The order in which things are done is kind of important)
By the way, does the popup citations work as they should in the draft for you? They don't for me, I. e. I don't get a popup, but the right thing happens when I click them. YohanN7 (talk) 16:54, 17 October 2014 (UTC)
Yes they work. By the way, the short hyphen you use in B-C-H wikilinks needs to be long, otherwise all these links go there through redirects. Also, the adjoin action link ends up on a disambiguation page... I'd use the algebra adjoint as opposed to the group one, since that's what you end up working with, anyway. I added W Schmied's free historical ref in the BCH article---maybe it belongs here too? Cuzkatzimhut (talk) 17:02, 17 October 2014 (UTC)

──────────────────────────────────────────────────────────────────────────────────────────────────── The baby proof is in place. It should be put in a note box, but this is problematic for me to test since I have this popup problem when i work in my user-space. YohanN7 (talk) 18:09, 17 October 2014 (UTC)

I put the central eqn in an eqnbox: I hope it is OK. Should I stick the baby proof in a collapsible box? I don't know their formal names. Cuzkatzimhut (talk) 19:02, 17 October 2014 (UTC)
I think it looks okay now. Thanks. I had though of a regular popup, but this is just as fine I guess. I'll move the page to the "creation area". It is already submitted, but it says in the top that it should perhaps be moved, so I'll do that. It might speed up the process. YohanN7 (talk) 19:32, 17 October 2014 (UTC)
The old link still works. YohanN7 (talk) 19:35, 17 October 2014 (UTC)

### Article in place

 Derivative of the exponential map Thank you so much for all inspiration, guidance and hands on editing. Getting so much help from someone truly brilliant in the field, and other fields too, I strongly suspect on good grounds, the result can't become any other than good. But I am overwhelmed over that kind of caliber barnstar. Thank you again. I hope the year of the wine is right. Chateau Cheval Blanc 1996 YohanN7 (talk) 00:59, 4 December 2014 (UTC)

Thanks. But, having checked on the internet the price a bottle of this fetches at auction, I am obliged to confess I have found clearance discount bin "poor cousins" of it for \$4.99 on occasion (luck; Chile, Portugal, Romania) which were actually good--with food. So, then, arguably the price equivalent of 50 bottles of those: At the rate of a bottle a week, that would amount to a year's supply... a heady supply, no? To think that my extremely distant (if not imagined) ancestors would trade wine to (alcoholic) Etruscan kings for slaves... getting heady already without the wine, there! Thanks again, Cuzkatzimhut (talk) 01:26, 4 December 2014 (UTC)

On a more serious note, I tried, and failed, to imagine alternate titles that some WP reader would try to find this type of stuff through, in a search, so as to fashion Redirects to this page... But with no luck... I cannot replicate the language one would use to search for it. In the past, I have seen things like that referred to as "Feynman's identity", which is a terrible cop-out... Perhaps Rossmann has pithy expressions on such? Anyway, I also stuck wikilinks to it in far-flung articles with clear conceptual links, but with no obvious handles to steer interested readers there. Cuzkatzimhut (talk) 02:04, 4 December 2014 (UTC)

dexp of course!
I was just about to ask someone how to create redirects. YohanN7 (talk) 03:19, 4 December 2014 (UTC)
And dexp it is.
Rossmann's book b t w was very well received. Anthony Knapp wrote a long very positive review, and even created an errata for parts of it because there were millions of small typo-like errors. The second edition is better in that respect, now only thousands of small errors remain. In spite of it being a senior undergrad/beginning grad level book in a mature subject it had novel approaches to proofs, especially of the Lie correspondence. YohanN7 (talk) 09:16, 4 December 2014 (UTC)

## S-matrix#Definition in quantum field theory

The talk about different Hilbert spaces for in and out states has been nagging me for some time. The QFT texts I have seen never expresses the possibility, and Weinberg's volume 1 (I have that one) is very clear, and emphasizes that all states inhabit the same Hilbert space.

I don't mean to burden you with anything here, but cold you at least say yes/no/maybe? YohanN7 (talk) 16:27, 5 December 2014 (UTC)

Oh, I really don't know, I shrug off any difficulties, and always agree with Weinberg, and "damn the torpedoes" (as RPF used to tell us). The torpedoes are normally obsessed on only by Haag's theorem types that I never run into.... (I'd rather attend a lecture proving the non-existence of fish. [1])
That is, different complete sets of states sharing the same Hilbert space, with S connecting them! I assume that, to do anything useful, some type of overlap of in and out states exists, whether nicely formulated or not, and all practical problems produce meaningful answers when transitions from in to out states are computed, and measured in our real world. As a rule, you know when you have an answer that makes sense... A friend of mine from graduate school kept emphasizing that "The theory is always smarter than you!". Cuzkatzimhut (talk) 16:44, 5 December 2014 (UTC)
I thought I said I don't want to burden you Thanks, now the article makes a little more sense. YohanN7 (talk) 22:06, 5 December 2014 (UTC)

## Perturbation theory (quantum mechanics)

The persistent attacks at this article by an anonymous guy from MIT started from Marco Frasca's blog and now is reiterating here. You can check the IP address to verify it comes from MIT. I think a better way to stop them is to stop the IP itself as this guy does not seem to be too much skilled on computer science.--Pra1998 (talk) 20:42, 10 December 2014 (UTC)

Thanks. As I indicated on my message on his talk page User talk:18.62.31.139 several MIT IP asses have been used, and it would be messy to be playing "whack-a-mole" with all of them and punishing potentially other users of them collaterally. I am not really interested in the subject of his beef, as it is barely intelligent, but editorial procedure must be followed. He has been put on notice, so he understands all future moves from an IP would be treated as plain vandalism. You may transfer this entire section/discussion to the talk page of the article. Cuzkatzimhut (talk) 21:02, 10 December 2014 (UTC)

## A question about in-line TEX on Wikiversity (NOT Wikpedia)

I am trying to write educational physics materials on Wikiversity, something I'm sure you appreciate, given all the well-intentioned efforts to insert mini-tutorials into Wikipedia. One issue that comes up on Wikipedia is the use of inline-TEX, which I use to compensate for the fact that equation numbers don't work well in wikitext (i.e., since I can't refer to previous equations by number I must describe them with words). In-line TEX is also fast to write, an important consideration for the highly underdeveloped Wikiversity. In other words, rough looking (but accurate) prose on Wikiversity is better than no prose. I understand from a recent comment you made, that some browsers poorly display inline-TEX. So I have two questions:

1. Do these inline-TEX incompatible browsers render the prose unreadable, or merely ugly?
2. Are these inline-TEX incompatible browsers obsolete (i.e., being phased out), or are they "the wave of the future"?

--guyvan52 (talk) 15:46, 18 December 2014 (UTC)

Apologies for my technical ignorance... I don't know what templates or workarounds Wikiversity employs, in contrast to Wikipedia... If it used all the WP gadgets, however, it could also use numbered formulas, as exemplified, e.g. in Derivative of the exponential map here.
Now, concerning in-line TeX, it is merely Uuuuugly, and slow (since graphics have to be imported and spatchcocked in like a ransom letter, differing in size, line justification, etc, from the normal text). If you emailed me, I could, privately, email you back screenshots of the look and feel. But it is certainly readable---there are no strictly inline TeX incompatible browsers (but those are not obsolete, they are just not Microsoft!). In WP it is deprecated, since it is meant to be read from tablets, iPhones, old browsers, etc... It is meant to be universal. Unfortunately, the math templates or in-line HTML symbols rely on font symbol collections of different browsers that now suffer by flakey collections of fonts/symbols, sometimes missing from several operating systems.
To experience some issues yourself, you might go to your WP Preferences>Appearance ...section Math , and click alternate boxes on several options , PNG, MathJax, etc... to see how inline TeX or HTML or formulas get to look... The problem there is that you may optimize these settings for one machine, but not for 4-5 that some use in the course of their day, and you readers of course.
HTML is "faintly" preferable in WP, as more universal, but there is divergence of opinion there, so maybe you wish to research the issue further. However, if your math symbols in HTML or templates look ugly (check them vs the left column of List of mathematical symbols), you might go to your WP preferences and chose suitable fonts, etc... I believe the future will include increasingly richer font/sets of glyphs etc... in most systems, even though I am a bit clueless about iPhone OSs... Cuzkatzimhut (talk) 16:21, 18 December 2014 (UTC)
MathJax is supposed to be the wave of the future, but we are definitely not there yet. It is meant to address inline TeX ugliness issues. Cuzkatzimhut (talk) 16:28, 18 December 2014 (UTC)
Thanks for the info. FYI, there is another reason for using inline-Tex. This Equation sheet is intended to be printed out as a pdf file for students to use as they take a first-year college physics course. Since each professor emphasizes different topics, it is important that this sheet be editable. (Wikiversity encourages parallel pages, even poorly written ones if they are done by students.) The use of inline text permits the equations to be presented in the most compact form possible. The intent of the equation sheet is that students studying for an exam not bother with memorizing equations; my best students know the material so well that they almost never refer to the equation sheet. But having it allows them to not worry about whether or not to memorize an equation.--guyvan52 (talk) 16:33, 18 December 2014 (UTC)

No argument there! I am a great fan of inline formulas. Indeed, for wikimedia my preferences of Math rendering were set to PNG, which made your page look Terrible, indeed, distracting (on a Yosemite OS Safari browser), but MLL etc makes it look tasteful. In that sense the future will improve compatibility. But doesn't Wikiversity support WP math templates? PS: I just checked it does! Cuzkatzimhut (talk) 16:44, 18 December 2014 (UTC)

Yes, MML almost gets it "right" on Firefox/XP too. By the way, does anyone know how to produce ${\displaystyle {\hat {f}}}$ in HTML? The obvious template (hat) does something completely different. But wait...; û, ..., ^f..., damned! YohanN7 (talk) 17:14, 18 December 2014 (UTC)

ƒ̂ , , , , , ƒ̂ , and sundry reminders i have jumbled in my sandbox.... Cuzkatzimhut (talk) 17:22, 18 December 2014 (UTC)

BUT look at what happens to the above under continuous magnification, positive And negative.... Cuzkatzimhut (talk) 17:43, 18 December 2014 (UTC) There is also the world of stuff ... Cuzkatzimhut (talk) 19:28, 18 December 2014 (UTC)

These look pretty good; ĝ, ĥ, but, alas, an f with a circumflex is what we need the most (Fourier transform). YohanN7 (talk) 21:27, 18 December 2014 (UTC)

## VB update

To let you know, the "last resort" regarding VB didn't respond. (The first two were very helpful and quick to respond.) As a parenthetical remark, I find some copyright laws around pretty absurd. It isn't exactly like VB himself is allowed to object to having his picture giving glory our articles. YohanN7 (talk) 23:27, 28 December 2014 (UTC)

Bummer... I am not surprised, in my cynical take of this lawyer-infested world... It is indeed bizarre to not have free access to what any google Image searcher could instantly access themselves! I have had a similar confusion. Achilles Papapetrou is missing a pic, but its russian analog, ru:Папапетру, Ахиллес has had less squeamish editors, who somehow stuck that one in... If only I knew how to transfer/ wikimedia-move/ transclude it to the english version... If I were up to squabbling, I might try a fast one with VB, hoping for the best.... Cuzkatzimhut (talk) 00:18, 29 December 2014 (UTC)

They did answer now, equally politely, after having searched through the boxes with VB's papers where it conceivably could have been found. Maybe I should make this my life mission? Legally obtain a photo that a 9-year old could arrange in a split-second. Sigh! YohanN7 (talk) 01:20, 2 January 2015 (UTC)

Seriously, I think an article without a good history section and a picture or two of the most prominent persons involved is lacking something. Preferably, there should be an anecdote or two as well. Just a naked publication date of the seminal paper in question feels rather dry. I have fairly recently gained access (through WP) to the natural sciences publications of the Royal Society (it's great, lots from the 30's, 40's and 50's is directly relevant for what I mostly have been writing about here), and I'll get full access to JSTOR in the days to come (and hopefully Elsevier's physical sciences later on). But I failed to apply for access to the history of science publications. I regret that. YohanN7 (talk) 01:32, 2 January 2015 (UTC)

Can you clarify your reason for this edit? Of course linearity is essential to the subject of the article, but why is it relevant to the use of "powers" in reference to iterative application of the operator? I am at a loss to see any connection. The editor who uses the pseudonym "JamesBWatson" (talk) 17:08, 29 December 2014 (UTC)

OK, I should think it is self-evident: It is extremely important in my mind to contrast to iterated functional composition, which is aggressively nonlinear and thus amenable to very different techniques, and, indeed, culture. A fractional index is just a point on a continuous trajectory, and should not warrant any confusion with functional iteration flows. (Personally, I believe the bloviation on functional composition there to be unwarranted, but if it evokes something for somebody, let it be.) But it is important to remind the reader up front that this entire article is about linear transforms, and any confusion to nonlinear contexts is counterproductive, especially to computer simulators. I do not recall the history of this, but there has been a persistent quasi-vandal insisting on cross-linking functional trajectories to fractional calculus, as through the reader will get a deep idea out of this confusion, somehow. Help, if you think you could prevent the confusion.... Cuzkatzimhut (talk) 17:46, 29 December 2014 (UTC)
My curiosity brought me there, and I'm totally unfamiliar with the subject. But it struck me, there is a place or two where operator appears unqualified with linear (and I don't mean D or J). YohanN7 (talk) 18:08, 29 December 2014 (UTC)
It would be nice if you could then qualify those... As I indicated, I personally find the bogus connection to functional iteration as the source of the problem. If that parenthetical (footnote) tangential analogy went away, the issue of linear operators or not would have never arisen in this article--nobody would take the left turn. But the entire article is clearly about differential and integral style operators, not the hellish maps of functional composition--not even the much much simpler Legendre transformation, and the reader should not get ideas.... Cuzkatzimhut (talk) 18:18, 29 December 2014 (UTC)
Ok, will do. Keep an eye on your watchlist for bogus edits. As I said, I have no clue about the subject. YohanN7 (talk) 18:35, 29 December 2014 (UTC)

Another query. This one I can't figure out: Rotation matrix What is the (vector?) A in section Exponential map? Also (unrelated but related) is there a half-angle version of Rodrigues' rotation formula on matrix form? YohanN7 (talk) 23:54, 30 December 2014 (UTC)

I'm not sure where the trouble might be... Isn't A the 3-vector defined in the previous section, 9.2, with components being the three matrices Ax ...? and then applied to 9.3? (so that u is the unit vector k and ${\displaystyle {\tilde {\boldsymbol {\omega }}}}$ was/is ${\displaystyle \theta \mathbf {K} }$.
Uhmmmm... are you sure it is unrelated? The formula in 9.3 in RotationMatrix is the same as the one in Rodrigues' rotation formula except for the half angle representation of the former. It is an inside "secret" in angular momentum that, even though integral spin reps such as the 3 dim one here, have periodicity 2π, rewriting them in terms of half the angle of rotation, with these half angles having periodicity 4π, perverse as it might look, is in fact useful, as the systematics of all reps, half And half integral spins are best systematized in terms of these half angles, so one does not flip from angles to half angles going from integral to half integral spins... It is nothing beyond plain rewriting at the level of the 9.3 formula, of course... Cuzkatzimhut (talk) 00:24, 31 December 2014 (UTC)
Sorry, this is all my mistake. I couldn't make sense of the A because it is gone in the present version from 9.2. By "unrelated" I meant that I didn't fully understand even with the A question out of the way and threw in a question about the possibility that there might be a Rodrigues' rotation formula for half-angles. I got lazy, couldn't find my old Spiegel MH with the trig-formulas. (Don't use the often enough to have them permanently in my system). But now you have answered in the affirmative. Thanks.
I hope I have time to straight this out in the article today, because now it is very hard to decipher with A gone. But it is new years eve... YohanN7 (talk) 10:28, 31 December 2014 (UTC)
I think the article may be okay now. But the tildes over u didn't make sense (I think). Happy new year YohanN7 (talk) 11:45, 31 December 2014 (UTC)
Happy New year--to come. I am not hands-on in this, but among these 4 articles, there are all these symbols that are the same but sometimes undefined... So ${\displaystyle {\tilde {\boldsymbol {\omega }}}}$ in Rotation matrix is undefined there, and only defined in the article wikilinked, K in Rodrigues formula is u.L, etc... Right now, as the reader clicks from article to article to find definitions, his/her head might spin---did I make a pun? In some cases, really all, putting the explicit expression θ u.L in the exponents for ${\displaystyle {\tilde {\boldsymbol {\omega }}}}$ in the exponents might save a lot of grief...Cuzkatzimhut (talk) 12:35, 31 December 2014 (UTC)
Yep, unification of notation across is a good idea. Unable to edit for a day or two now. (I did fix Rotation matrix.) YohanN7 (talk) 13:26, 31 December 2014 (UTC)

Why did you revert this edit? The reversion wasn't given a summary. To my knowledge, my edit was correct and added significant information to the page. (Sorry, I don't know how to sign this comment, I'll look back here to see if there's a reply.) — Preceding unsigned comment added by 24.12.4.162 (talk) 19:44, 11 July 2016 (UTC)

This is a different discussion, in which you chose to insert your comment. You should have started a new item at the bottom of the page. Signing takes typing 4 tildes , ~, in succession. Your edit is, of course, correct, but trivial, as it definitely does not add significant information to the page. It is, at best, a superfluous footnote, which might have actually survived as a footnote. Barrelling down all calculus formulas and pointing out the obvious fact that they can be generalized to higher dimensions when dealing with Cartesian product arrays hardly enhances readability. If you have a radically informative and nontrivial section on higher dimensional generalization, you might finesse sections 9 or 8, or.... But breezy comments at the introductory level of definitions are normally frowned upon. I would urge you to get an WP:ACCOUNT. Cuzkatzimhut (talk) 20:11, 11 July 2016 (UTC)

I could not find anywhere in Wikipedia the fact I mentioned, where one could have ${\displaystyle h=(1,2)}$, for example, in ${\displaystyle {\mathbb {R}}^{2}}$, and I wanted to reference it from another site. As for the content and tone of the rest of your remark, do you really want to discourage occasional contributions from professional mathematicians? 24.12.4.162 (talk)

Wikipedia certainly welcomes off-the-cuff contributions from anyone, professional or experienced enthusiast, provided they be salutary. But I am alarmed you believe an anodyne result on self-evident generalization possibilities belongs right in the introductory section and not in sections 9, 8, a section of your own choosing, as I also mentioned, but evidently you disapproved of the content. However, that is precisely the point of the article's Talk page. Had you broached your proposal in the talk page before the edit, instead of my page, in the wrong section, much of this miscommunication would have been avoidable. But that is part of the point of my urging you to get an account. Do you wish to ignore this and proceed with cogent proposals in the Talk page which will be properly evaluated by the community of the page's editors? And, again, please sign your edits, even as a sign of goodwill. The IP and its location, are manifest to Editors, as you appreciate. Cuzkatzimhut (talk) 22:38, 11 July 2016 (UTC)
A small point on etiquette. Inline TeX is easy to write, instead of html, but, as you saw, substituting the ${\displaystyle i}$ with i or i in HTML avoids ferocious multiplatform problems on a broader array of systems... Even if inline TeX looks good to you, it might come across as unreadable or a ransom letter to other platforms, especially old ones... WP is a resource for the whole world... Cuzkatzimhut (talk) 22:51, 11 July 2016 (UTC)

## Wavefunctions for particles with spin

Hi, excuse the favour, but user:YohanN7 and myself have had a discussion on how to clarify wave functions for particles with spin; particularly on domains and codomains, and the decomposition into a product of a space function and spin function (when possible). It seems badly covered in the literature, but it's no reason for the WP article to be just as unclear.

We have reached a conclusion, and intend to edit the actual article, but before we do a third opinion and your expertise would be valuable. I ask here given your collaboration with Yohan and because of your activity on the Pauli matrices article.

Thanks! ^_^ M∧Ŝc2ħεИτlk 17:35, 12 January 2015 (UTC)

Humph... Nothing in the Pauli matrix article should warrant an opinion on this... And I really fear I cannot reconstruct the whole conversation with its winding turns and twists in a short time... So, if you are just asking whether the green hidebox is fine, yes, sure, it's fine---I might have said "complex two-vectors (two-spinors)" instead of "complex vectors", myself. But I don't want to get involved into subtle discussions of when the space part and the spin part factor out / decouple / ignore each other:⊗.... These are all, after all, special limits/rewrites of the fully coupled relativistic Dirac spinor... quite well described in JJ Sakurai's Advanced Quantum Mechanics, actually. (In any case I linked L&L online at the Pauli article, but now i see you already did that too!) The space part and the spin part start coupling in atomic physics spin-orbit coupling, i.e., the term σ⋅L (a Pauli vector!) in the Hamiltonian, where that level of accuracy is required, tells you the space part and the spin part "talk" to each other and coordinate to reach eigenfunctions of the full hamiltonian including that term---otherwise, they'd not talk to each other:⊗. Did I come close to grasping what is troubling one? Cuzkatzimhut (talk) 20:18, 12 January 2015 (UTC)
Yes... Thanks for reminding about spin-orbit coupling, now the condition is clearer (any coordinate-dependent entity coupled to the spin operator prevents the factorization, a.k.a any coordinate-dependent Pauli vector in the Hamiltonian), and for the pointer to Sakuari (which I used to have access to at uni, but not anymore).
You're confirming exactly what the sources say, that the wavefunction can be written as a complex vector, which is fine, but Yohan is saying it's just a complex number as a function of spin and space and time, or a complex vector with space and time dependence only. This is the core of the discussion.
Finally... reference to Pauli matrix since you were discussing higher spins on the talk page there.
I'll not clutter your page further. Cheers! M∧Ŝc2ħεИτlk 21:02, 12 January 2015 (UTC)
Yohan is saying that the wave function as a function on coordinate space and spin z-component is complex valued, not vector valued. If you lump together these values for different z-components of spin for the same spacetime point, then you can organize them in a column vector if you want to. This is something different. You confuse
${\displaystyle \Psi (\ldots ,1/2)\in \mathbb {C} }$
with
${\displaystyle \left({\begin{matrix}\Psi (\ldots ,1/2)\\0\end{matrix}}\right)\in \mathbb {C} ^{2}.}$
Furthermore,
${\displaystyle \left({\begin{matrix}\Psi (\ldots ,1/2)\\\Psi (\ldots ,-1/2)\end{matrix}}\right)\in \mathbb {C} ^{2}}$
is the wave function evaluated at two points in the domain. When sloppy (standard) you might write
${\displaystyle \Psi (\ldots )=\left({\begin{matrix}\psi _{1/2}(\ldots )\\\psi _{-1/2}(\ldots )\end{matrix}}\right)\in \mathbb {C} ^{2}.}$
(no spin arguments on the left, but present as an index on the right) and call it vector-valued. This latter is not going to help the mathematically inclined who have been asking about domain and range. YohanN7 (talk) 21:44, 12 January 2015 (UTC)
Here is what I just said (or at least meant), which echos what you wrote here and here:
"a complex number as a function of spin and space and time" ${\displaystyle \Psi (\ldots ,1/2)\in \mathbb {C} }$
"a complex vector with space and time dependence only" ${\displaystyle \left({\begin{matrix}\Psi (\ldots ,1/2)\\0\end{matrix}}\right)\in \mathbb {C} ^{2}.}$
so how does that mean I confused the two in reply to Cuzkatzimhut? And please, let's keep this on talk:wave function, the post above was a simple question. M∧Ŝc2ħεИτlk 21:58, 12 January 2015 (UTC)

Oh, dear, as I said, I am very bad in replicating what others thought, when, etc.. in a convoluted appeals case! I seem to be agreeing with everyone, which might mean that I am missing a point, or not... In any case, I completely agree with the "sloppy"

${\displaystyle \Psi (\ldots )=\left({\begin{matrix}\psi _{1/2}(\ldots )\\\psi _{-1/2}(\ldots )\end{matrix}}\right)\in \mathbb {C} ^{2},}$

above, and hardly imagine it could confuse anyone. I am completely confused about any (presumed??) practical difference (skipping t) between (x,i) ↦ c and x ↦ (c1, c2) for i a bimodal variable, =1,2 and c's complex numbers... Is there any? Cuzkatzimhut (talk) 23:36, 12 January 2015 (UTC) Trip cancelled. Thanks to Maschen for move of higher spin matrices. To my surprise (well, perhaps not really, given the caliber of the guy...), Willard Gibbs was teaching the Pauli vector composition formula to his students in 1884, "essentially", before Pauli matrices, before Engø, of course, and without the benefit of quaternions, even... I added the ref, but not the link to the free copy of the IInd volume of his collected works on Google books. The things one learns at the end of the day...Cuzkatzimhut (talk) 20:16, 13 January 2015 (UTC)

## A content question on Compton scattering images

Hi - I have an issue with a number of images pertaining to Compton scattering. If you think you have any insights, please visit:

Thanks - --guyvan52 (talk) 17:37, 18 February 2015 (UTC)

Apologies, no time, no interest. Cuzkatzimhut (talk) 18:09, 18 February 2015 (UTC) But it is certainly the case that the angle between the scattered electron and photon is not π/2 in general. For, if they were, look at the awful constraint m=ν' (in natural units, ħ = c = 1) this would produce, when you equate momenta in both directions.... Cuzkatzimhut (talk) 20:15, 18 February 2015 (UTC)
I will take your brief statement as confirmation that my drawing is correct. Thanks. I will worry about it no more. Keep busy! --guyvan52 (talk) 20:25, 18 February 2015 (UTC)
Yes. In point of fact, the exact expression for the electron angle φ as a function of the outgoing photon angle θ that is often used in undergraduate lab courses (and can be found in Adrian Melissinos' book) is, again in natural units, cotφ = (1+ν/m) tan(θ/2). You may thus "dial" yourself a φ to be distinctly different than the π/2 complement of θ by choosing a suitable incoming photon frequency. Cuzkatzimhut (talk) 01:41, 19 February 2015 (UTC)

## References

Could you please add some references to Scalar field theory, where they belong. That would be great, thanks. And maybe expand here Solutions of the Einstein field equations. prokaryotes (talk) 04:37, 13 August 2015 (UTC)

I did a minimal-compliance move of the classic/standard QFT texts to indicate that the entire following article is present in these standard texts, in overlapping increasing detail. There is not point in over-specific tagging one of them as opposed to the others... if the reader wished to know more, any of the texts in the reference section would provide the same information---and it would be unfair to future contributors to single any of them, by dint of notation, e.g., to serve as "the" source. Unfortunately, I see no specific subtleties requiring in-line chapter-and-verse citation. My sense is that if editors agree on the soundness and optimality of the exposition, it is up to the reader to go to any of the books to feel more comfortable about what they read. Cuzkatzimhut (talk) 10:50, 13 August 2015 (UTC)
The problem is i have to read now like 10 books, some older then 20 years to check if the article has it all right. Ofc we can cite books but then we should add a info about which page exactly contains the data, like page 20-30 are about the equations. WP articles follow some guide lines, and a good article has inline citations and references to easily follow up on the information. prokaryotes (talk) 14:02, 13 August 2015 (UTC)
No, that was not my point: any of the books will suffice, and any book's section on scalar field theory would do. The stuff is standard and "right" as you put it, and ancient, so contemporary books are hardly needed. Jordan did it all 80 years ago. The option to learn more is the reader's ... it is a little bit like requiring a "reliable source" for the Pythagorean theorem... But, in any case, I don't have the patience to annotate the whole thing... There must be another volunteer. (You have ascertained that I did not write any of it, right?) It is, however, reasonable, correct, elementary, and standard. I will do something useful, when I can, though. I will link to other articles that introduce the notion of a classical scalar field, which the reader must know cold before finding him/herself here, and the self-evident procedure that leads to its quantization, as Jordan appreciated in the 30s. This short article simply collects all the answers for quick reference. It is not, and should not be a tutorial. Cuzkatzimhut (talk) 14:19, 13 August 2015 (UTC)
The problem is also that the article is in part very poorly and unusual written (For instance last paragraph of lede), which again complicates reliability. I don't blame you on the entire article, but i looked at your recent edit, and it doesn't contain a reference. Notice that content which is not referenced might be removed or tagged for citation. prokaryotes (talk) 14:39, 13 August 2015 (UTC)
I half-agree that it is poorly written, but it succeeds in its major job of mapping the landscape and sending the interested reader to the main articles that explain what that reader wants to learn. The article cannot be a lightning introduction to a subtle subject, if the language of the subject is not already obvious to the reader. So I disagree the lede is obscure. The reader is supposed to know the language of relativistic Lagrangian field theory already (a "further" link I just put in) and to appreciate the conventions chosen right here. But, as I am sure you appreciate, all the issues summarized here have lengthy expositions in other articles. I frankly don't understand which unreferenced edit of mine you are referring to. My last half dozen edits are notational template copyedits...., no? Cuzkatzimhut (talk) 15:12, 13 August 2015 (UTC)
I suggest you read WP:TECHNICAL - Articles in Wikipedia should be understandable to the widest possible audience. prokaryotes (talk) 15:19, 13 August 2015 (UTC)
Yes, I've read it, of course; have been consulting it for about a decade. I'm sure you appreciate, though, that, in recondite technical subjects, the "widest possible audience" cannot encompass absolutely everyone, as not everyone can instantly grasp quantum physics, or else a marvelous opportunity to educate physics college seniors would have been lost! By the way, trashing the lede would puzzle such a reader, as they would miss the point that the west coast +--- metric is used here. Fine by me, but the notional clueless reader is guaranteed to suffer.... Cuzkatzimhut (talk) 15:30, 13 August 2015 (UTC)
There is no reason to state in the lede what metric may or not may be used by a citation which does not refers to a specific part of the content. Even if those refs were added to the correct place, the reference would already contain the required metrics. Thus the notice is superfluous in any sense. prokaryotes (talk) 15:32, 13 August 2015 (UTC)
You are not being terribly clear. When the reader reads the article they know the language but they wish to understand the usage. It is common practice to specify your metric when you start. You inserted a wrong statement in the lede about "closely related to QFT". The article starts by telling the reader that both classical and QFT are included. The eprint you adduced for QFT is rather bizarre. Please propose such radical changes in the talke page of that article for the remaing editors to vet. not here! Cuzkatzimhut (talk) 15:37, 13 August 2015 (UTC)
What is wrong about this statement, i edited an existing part. However it might be removed entirely. I second that we should use the talk page. See you there if you require discussion. prokaryotes (talk) 15:42, 13 August 2015 (UTC)
It is very-very wrong as i already argued there. Cuzkatzimhut (talk) 15:46, 13 August 2015 (UTC)

Notice that your edit here, does not conform with WP standards. If you want to improve reference please add them at the correct place, and add proper references. prokaryotes (talk) 16:34, 13 August 2015 (UTC)

You seem to misunderstand my edits. My edits are cosmetic copyedit template statements, which I doubt you'd wish to find referenced, and promotion of the preeminent references in QFT to the main reference of the article, as a response to your own very invitation, today, above. They are the most prestigious, current, and yes, "proper" references, and I thought I had convinced you of the point of excessive in-line fussing. Are you familiar with QFT, at all? What exactly is the problem? you want them demoted where they were before, and make them less accessible? You want the reader run to a cosmology article you adduce to educate themselves on QFT? You invite me to help you out and object to my spending time on this? Make up your mind. Cuzkatzimhut (talk) 16:43, 13 August 2015 (UTC)

## Your recent post at WP:AN3

See Wikipedia:Administrators' noticeboard/Edit warring#User:Prokaryotes reported by User:Cuzkatzimhut (Result: ). Your post doesn't follow the usual rules, in that it doesn't specify an article where you believe that edit warring has taken place. Please expand your report. You should include the names of one or more articles that show either a 3RR violation, or a pattern of long-term edit warring. A general complaint about the behavior of an editor belongs in some other place. Thank you, EdJohnston (talk) 01:50, 14 August 2015 (UTC)

Dear EdJohnston, as I directly indicated on that report, on Aug 13 User:Prokaryotes unleashed a rampage on half a dozen pages I had been editing, reverting my improvements and sprinkling unwarranted Refimprove templates in an incontrovertibly personalized campaign not even remotely feigning good faith. I do not see that WP would welcome reasonably good articles turning into construction sites with gaudy, crackpot, inappropriate template signage on them all for the misperceived benefit of teaching an editor a vituperative, if not unhinged lesson. WP evidently must have defenses against this abuse, but they are as clearly hard to access. WP should not implicitly encourage this type of mischief.
The reason I did not detail isolated instances is because, as indicated on that report, the pattern of abuse is self-evident and documented in perpetuity. It should be up to WP to detect and redress abuse, not up to me to build up a case for it. Cuzkatzimhut (talk) 12:35, 14 August 2015 (UTC)
I've proposed that your AN3 report should be closed. You can reply there if you wish. Thank you, EdJohnston (talk) 15:18, 15 August 2015 (UTC)

Well, Ed, I am not sure what to propose: In my mind, your board has grossly failed its mission. If there is another venue to address this destructive hounding, please do transfer the case there.

I originally invited you to identify the highly personalized rampage of Aug 13, UT 15:05 - 27:10, and the unwarranted gratuitous acrimony that followed, and to collectively restore the damaged pages, Adjugate matrix, Fermi's golden rule, scale invariance, special unitary group, non-linear sigma model, De Sitter special relativity, Rotation formalisms in three dimensions, canonical commutation relation, wave packet, Polynomial Wigner–Ville distribution, wave packet, pauli matrices, etc, all edited by me last, and that the livid rampager decided to "fix" in a breathtaking spasm of bullying petulance (can only email privately on this). I was hoping you'd realize than when references are summary deleted only to be supplanted by request for references templates, that should be an open-and-shut case.

After the "I don't know what you are talking about" treatment, I am giving up on your report board, and will try to redress the damage, by myself and with conscientious collaborators, laboriously, by hand. However, I should think WP deserves a better way of defending itself against such vicious rampages. It is not about me, and I ask for nothing myself. It is about stanching runaway loose-canon damage. You are aware, I assume, of lots of these little dramas that never reach you, but which routinely result to rather nasty damage to perfectly fine WP pages, negating lots of volunteer work---all wasted.

But if you investigated and failed to see the pattern, and wanted me to build up a lawyerly case for the obvious, I have no stomach for it. I will try to fight the good fight away from that disappointing board. Cuzkatzimhut (talk) 16:39, 15 August 2015 (UTC)

## Notice of No Original Research Noticeboard discussion

Hello, Cuzkatzimhut. This message is being sent to inform you that a discussion is taking place at Wikipedia:No original research/Noticeboard regarding an issue with which you may have been involved. Thank you. prokaryotes (talk) 13:36, 14 August 2015 (UTC) prokaryotes (talk) 17:11, 14 August 2015 (UTC)

## ANI

There is currently a discussion at Wikipedia:Administrators' noticeboard/Incidents regarding an issue with which you may have been involved. Thank you. prokaryotes (talk) 17:11, 14 August 2015 (UTC)

What's the deal, the edit warring forum and the OR noticeboard are not coming out to your satisfaction? Anyone with access to the record and a functioning mind can get to the issue of systematic abuse in no time. Cuzkatzimhut (talk) 18:33, 14 August 2015 (UTC)

## Some relevant policy

I believe that your edits are in good faith, and so are many of the other editor's. I linked this at WP:ANI but I am not sure if you and YohanN7 read it. You might want to read Wikipedia:Scientific_citation_guidelines#Uncontroversial_knowledge since it seems to pertain to your case. I am not qualified enough to judge how applicable it is to your case, but you might want to keep this in mind. Kingsindian  13:32, 31 August 2015 (UTC)

Thanks. Has there been a new development for 2 weeks? I suspect YohanN7 was turned off by the avalanche of nonsense.
I certainly read then, and quoted repeatedly Wikipedia:Scientific_citation_guidelines#Uncontroversial_knowledge, a couple of weeks ago in the 3-4 venues this conversation metastasized to. I have kept that manual page in mind, for 9 years. But I actually rarely write extensive chunks---I largely untangle or vet their sometimes shaky soundness and improve the logic and the message, adding more references where it is salutary. (A structural problem is novices avoiding the main tutorial articles and going to hyper-technical articles/stubs whose language they barely understand, and expecting to achieve running competence in 5 mins right there... Somehow, they don't do this to math articles, but they expect that physics, since it uses words, would somehow be easier or obvious to grasp subtleties of. They then attribute the disconnect to flaws of the article itself.)
My primary concern, as explained, is to avoid insertion of misleading or unsound material in the articles and to avoid deletion of standard knowledge with extant "uncontroversial knowledge" pointers which can support verifiability, and which can always be improved. As I have indicated, the ploy of peremptorily removing material under the guise of misconfigured or expired links (as in Pascual Jordan Aug 13) without crucial discussion in the Talkpages, is far too familiar, in my experience, to merit lengthy debate. Cuzkatzimhut (talk) 14:52, 31 August 2015 (UTC)

## Frank Kenneth Goward

This is an automated message from CorenSearchBot. I have performed a web search with the contents of Frank Kenneth Goward, and it appears to include material copied directly from http://www.goward.com/Frank%20Kenneth%20Goward.htm.

It is possible that the bot was mistaken and found similarity where none actually exists. If that is the case, you can remove the tag from the article. The article will be reviewed to determine if there are any copyright issues.

If substantial content is duplicated and it is not public domain or available under a compatible license, it will be deleted. For legal reasons, we cannot accept copyrighted text or images borrowed from other web sites or printed material. You may use such publications as a source of information, but not as a source of sentences. See our copyright policy for further details. (If you own the copyright to the previously published content and wish to donate it, see Wikipedia:Donating copyrighted materials for the procedure.) CorenSearchBot (talk) 18:34, 26 January 2016 (UTC)

## Speedy deletion nomination of Frank Kenneth Goward

If this is the first article that you have created, you may want to read the guide to writing your first article.

You may want to consider using the Article Wizard to help you create articles.

A tag has been placed on Frank Kenneth Goward requesting that it be speedily deleted from Wikipedia. This has been done under section G12 of the criteria for speedy deletion, because the article or image appears to be a clear copyright infringement. This article or image appears to be a direct copy from http://www.goward.com/Frank%20Kenneth%20Goward.htm. For legal reasons, we cannot accept copyrighted text or images borrowed from other web sites or printed material, and as a consequence, your addition will most likely be deleted. You may use external websites or other printed material as a source of information, but not as a source of sentences. This part is crucial: say it in your own words. Wikipedia takes copyright violations very seriously and persistent violators will be blocked from editing.

If the external website or image belongs to you, and you want to allow Wikipedia to use the text or image — which means allowing other people to modify it — then you must verify that externally by one of the processes explained at Wikipedia:Donating copyrighted materials. If you are not the owner of the external website or image but have permission from that owner, see Wikipedia:Requesting copyright permission. You might want to look at Wikipedia's policies and guidelines for more details, or ask a question here.

If you think this page should not be deleted for this reason, you may contest the nomination by visiting the page and clicking the button labelled "Contest this speedy deletion". This will give you the opportunity to explain why you believe the page should not be deleted. However, be aware that once a page is tagged for speedy deletion, it may be removed without delay. Please do not remove the speedy deletion tag from the page yourself, but do not hesitate to add information in line with Wikipedia's policies and guidelines. Qpalzmmzlapq (talk to me) 20:28, 26 January 2016 (UTC)

## Green's function vs. fundamental solution

I've been editing the table at Green's function with some more edits planned. I noticed you have been editing fundamental solution. The two articles don't seem very different to me, apart from the greater development of the Green's function article. The first few sentences of the two articles mention that boundary conditions are the difference, which is somewhat weak of a difference given that you would usually integrate/convolve a Green's function or fundamental solution over some boundary, use the method of images, or do something like that in either case. Is there some historical distinction that's important? Or is it worth merging these articles? There's also the throw-away article method of fundamental solutions.

By the way, please check my work in the table. I had been mostly inspired by equation 16 of [2] while solving the 2D version for a ballistic+diffusive model that I needed. I tried to adjust the prefactors of the deltas in the solutions to the parabolic and hyperbolic equations integrate to 1 in each time slice following the example. For the Klein–Gordon equation, this is maybe weird because you usually want the integral of the square to be 1. Teply (talk) 08:11, 22 March 2016 (UTC)

Yes, yes, yes! Go for it. I 've always thought that multiplexing is absurd, based on tribal, cultural, and vanity/control grounds... The Green's fctn one started in 2003, the Fund soln in 2005, and the Method one in 2012. I may have contributed to the absurdity of the distinction involving BCs, trying to sharpen it--you find it repeatedly in British books of the abstract/distribution type, pretending to break off from 19th century applications and engineering, focussing on snobbish French-style abstract mathematical structures. Since there is so much ebb and flow and interference, I have opted for playing on several pianos, sniping and fussing limited items, as is easiest for most. If you have the time, energy and concentration needed to merge, go ahead, as few can do it like you!
The only meek defense for multiplexing I could think of, is strategic/sociological, and it is admittedly poor. Time and again, articles or sections fall into the hands of insistent influence groups or individuals with an ax to grind, so having several platforms to salvage and insert worthy points, little Switzerlands, might be useful--I have experienced this in addressing Physics stack exchange complaints about WP articles... I go back to see how they could have been misread and improve them, but I can easily spread improvements and nuggets out of harm's way. (An egregious example of this is the coefficients of the characteristic polynomial of a matrix, in determinant, Cayley–Hamilton theorem, and, my evident favorite!, Faddeev–LeVerrier algorithm. While this multiplexing is suboptimal, still, a motivated reader can channel-flip to get what they might be seeking.)
So, good luck with your project... Will look at the table, but don't expect too much from me... However, I'll look at the consistency and limits of the entries to each other, and report back to you. PS. there is also the penumbral Propagator. Cuzkatzimhut (talk) 12:29, 22 March 2016 (UTC)

## Microstate in phase space

Hello - I added a section to Microstate (statistical mechanics) entitled "the microstate in phase space" subsection "Classical mechanics". I have been concentrating on classical thermodynamics lately, and I am not ready to describe the microstate in quantum phase space. If you are so inclined, I think it would be a good addition to the article. PAR (talk) 23:07, 30 March 2016 (UTC)

Hi, thanks for the implicit flattery of the invitation, but I'd have nothing to add constructively as a new section, beyond some platitudes of elementary cells of size ${\displaystyle \hbar ^{3N}}$ or something, mumbling that the uncertainty principle reserves cells of this size for a particle... and maybe link to Quantum concentration. But ultimately the bulk of the discussion should end up in the Bose-Einstein distribution and Fermi-Dirac distribution...
I'm not up to it right now, but I'd be happy to vet or tweak anything you put in; but a whole new section contradistinguishing the counting and the combinatorics might be too much, to my taste--possibly a paragraph at the end of the classical section might suffice... There is a subtlety of quantum entropy in phase space involving the ħ normalization of the dp dq / ħ phase space volume element, but its place to be explained is not in this article, I fear... Cuzkatzimhut (talk) 00:11, 31 March 2016 (UTC)

## Fortifying wikiquanta

Hi, I seek volunteers for this. Boris Tsirelson (talk) 18:09, 15 April 2016 (UTC)

Looks like a good cause, but no memorable book jumps at me... I have my hands full at the moment, but will think about your quest. In some sense, I am a bit blase' about this... I had Feynman's volume III in college in the spring of 1971, and have not succeeded in questioning any of his pedagogical schemes and assertions there since... so have spent almost half a century scratching my head as to why people seem so metaphysically conflicted about QM... and what the fuss is about, really. Following the math, I have always thought these issues were settled before Acton's or EPR type experiments, Bell's inequalities, etc... (even though I am delighted by clever new schemes confirming orthodoxy like the Delayed choice quantum eraser.) Quantum computing types are breathing new life into this, but the issues have been settled in my mind for so long that they have become dull for me... almost as dull as arguing about the round earth... Will try to stay in the loop, making small, salutary changes when and where I could. Thanks, Cuzkatzimhut (talk) 19:14, 15 April 2016 (UTC)
Interesting! Are you a counterexample to the "rule" that those who are not shocked by the quantum theory did not understand it? Boris Tsirelson (talk) 20:22, 15 April 2016 (UTC)
I guess I am... I am happy with the part I do understand, and I see no reason to seek trouble. I mean, after 90 years of unremitting success and clearly bogus, harebrained, or worse, pseudo paradoxes, one would expect spirits to have calmed down— they actually largely have, in the professional community of users of QM. Since I am not interested in philosophy or psychology I would not get into the mode of how people keep on getting confused by Schr's cat nonsense and misconceptions... There are deeper mysteries to understand out there. Cuzkatzimhut (talk) 21:35, 15 April 2016 (UTC)
In order to "centralize" the discussion I've copied this to my talk page; hope you do not object. Boris Tsirelson (talk) 13:30, 21 April 2016 (UTC)
Cool! Cuzkatzimhut (talk) 13:46, 21 April 2016 (UTC)
Are you also following the mayhem on Talk:Observer effect (physics)? Cuzkatzimhut (talk) 11:06, 8 June 2016 (UTC)
It is perhaps best to meet it with silence. I think there actually have been speculations (presented as more poetry than actual truth) about "conscious observers" by reputed physicists way in the past. I have not pursued it beyond the brief mentions in the chapter typically named "philosophical problems" (or the like) in basic QM books. I really don't want to touch it – and it is a different "observer effect" than the article is dealing with. Maybe a mention in history of quantum mechanics or interpretations of quantum mechanics would be warranted? That could perhaps satisfy the present poster if he persists. But I don't know. YohanN7 (talk) 13:43, 8 June 2016 (UTC)

## IP editor comment

Hi-You should go to the editorial assistance/request noticeboard; an IP user mentioned some edits you reverted. This would be under the heading of Predatory behavior towards IP user. Many thanks-RFD (talk) 12:51, 2 June 2016 (UTC)

I'm not sure what you expect me to do. The allegations are meritless: hiding behind several IPs from the Dallas area, there has been unwarranted and mostly unsound/misleading snipes at the page, which I have been restoring, all the time inviting the determined IPs to discuss the issues first, if they believe there are issues. Mischaracterizing vigilance as "predatory behavior" (Wikipedia:Editor_assistance/Requests#Predatory_behavior_towards_IP_users) instead of discussing, in the self-righteous expectation that this is OK and proceeding with increasingly loopy edits because "they can't get caught" can hardly help their case. Getting an account where they can be talked to, responsibly and accountably, would be best. Cuzkatzimhut (talk) 13:01, 2 June 2016 (UTC)
Hi-The IP never bothered to let you know of the posting. I have had some run-ins with some IPs and it was not pleasant. Many thanks-RFD (talk) 15:44, 2 June 2016 (UTC)

Thanks. I asked them the obvious question: if consensus is the central pillar of WP, how do you achieve consensus with anonymous figures who refuse to talk to you?. Cuzkatzimhut (talk) 03:40, 4 June 2016 (UTC)

## ANI Notice

There is currently a discussion at Wikipedia:Administrators' noticeboard/Incidents regarding an issue with which you may have been involved. The thread is To whom it may concern. Thank you. General Ization Talk 03:59, 3 June 2016 (UTC)

## Jacobi formula for gradient of determinant

Hi, you recently reverted my edit to the Jacobi's formula page:

You are right, the special case does appear in the proof; I admit I did not read the proof. How do you feel about calling out the special case somewhere, so lazy people don't have to search for it in the two page proof of the general formula?

I just added the special case to the intro:

Does that seem reasonable?

And why do I think this special case is important? I need it because it comes up when you take the gradient w.r.t. the matrix elements of formula involving the determinant of that matrix. This comes up when try to use gradient ascent to optimize such a matrix formula. For example (not my question or answer, but the ntc2 comment is mine):

In my case, I need to optimize the likelihood of a multivariate normal:

Enoksrd (talk) 19:26, 5 January 2017 (UTC)

OK, your addition in the lede is plausible and salutary ... and foreshadows the reversible logic of the expression when used in the proof later. Cuzkatzimhut (talk) 19:45, 5 January 2017 (UTC)

## Weinberg angle graphic

Please see here [3], thanks MŜc2ħεИτlk 09:02, 21 February 2017 (UTC)

Much obliged...Linked it all over the place. I can hear the hapless students' sighs of relief.... Cuzkatzimhut (talk) 14:43, 21 February 2017 (UTC)

## A quasi-distribution associated with Born–Jordan quantization

Hello Cuzkatzimhut, I noted a recent article on using the Born–Jordan quantization in place of Weyl quantization, and on a redefinition of phase space quantum mechanics, in which the Wigner distribution is replaced with another quasi-distribution associated with Born–Jordan quantization (The Angular Momentum Dilemma and Born–Jordan Quantization). It's an article by Maurice A. de Gosson, and certainly to be taken seriously. I was wondering whether you see something of value for the Wikipedia article on phase space formulation? I am out of my waters here and was thinking you may see more clearly on this, or might know about it already. --Chris Howard (talk) 19:51, 11 June 2017 (UTC)

Personally, I don't see anything of value in using WP eyeballs to attract attention in that direction. As you probably know, quantization (producing QM operators out of classical observables and variables) is an art, and should be kept out of any and all association with the actual objective phase-space formulations.
These are mere changes of representation, all equivalent, and perfectly, systematically, and seamlessly interconvertible to each other. So it is a matter of taste and technical convenience which prescription one uses: Weyl, Mehta, Husimi, Born-Jordan, etc. The serious danger in inserting B-J is that the author of that paper "champions" it, assuming, erroneously (I believe), that some prescription is "better" than any other, because it makes a quantization scheme "better", etc... There is, however, a theorem (the Groenewold- van Hove thm) that there is no "good" (adequate) quantization scheme. Preference of one is subjective, and, ultiely, pointless: a quantum hamiltonian that works for one purpose has a classical limit that possibly other quantum Hamiltonians share, which might be more suitable for other systems. It is a bit like asserting that Nature prefers a coordinate system over another. Inflammatory language such as "inconsistency", "dilemma", "paradox", etc.. are there to confuse the confusable.
Phase space quantization is well-understood and all "problems" evoked in these discussions are misguided (You asked my opinion...). In any case, you might try to make a separate stub on it yourself, given your editorial association with MdG... Maybe this sort of thing belongs in the footnotes of Quantization (physics), but as Dirac used to put it, it should be "prepared to meet stiff criticism". In any case, any effort should be made that the ordering prescription part in the phase-space formulation of it be kept logically disjoint from the quantization map--same math, enormously different function of it. Cuzkatzimhut (talk) 22:00, 11 June 2017 (UTC)
Thank you for your answer. Indeed the topics of quantization and dequantization are topics on which there is much to say and with pitfalls, as shown already by Groenewold and Hove, and form an area of research on their own. My question was mostly the expression of my hope that with your knowledge of phase space quantization, which you refer to as well-understood, you might also shed some light on these topics, with MdG's paper being the occasion for my question. I gather that at least with "WP eyeballs" you do not see much potential there. I appreciate your stating your opinion here. I do agree that Quantization (physics) could be explained more, be it by footnotes or otherwise. For example along the lines of the introductory portions of the articles doi:10.1142/S0129055X05002376 [4] and doi:10.1007/978-1-4612-1246-1_7 [5]. If you have any further comments, they're always welcome, otherwise it's fine and thanks again. --Chris Howard (talk) 10:02, 15 June 2017 (UTC)
Ah! I appreciate the confusion. "Phase space quantization" or "Deformation quantization" are not quantization procedures, however perverse the terminology may be! They arose in the context of quantization, but soon both Moyal and Groenewold, and most of their followers, (certainly always Wigner), understood it as a mere bland representation change. The community continue to refer to this representation change as "phase-space quantization", because, given a chosen quantum theory, the Wigner map represents it in phase space, where its systematic ħ structure is easier to investigate as a "deformation" of the classical theory. It might be less confusing to call it something like "deformation to the classical theory" or something of the sort. But, nowhere is the Wigner transform of the quantum theory derived out of (a Weyl map or a BJ map, or... of) the classical theory: it is a phase-space representation of a given quantum theory that arose through "art", or a mystery, as Todorov puts it, and experiment dictates it, not a theological principle of stretching classical physics.
Formally, it is straightforward: Take a classical observable f. In the Weyl quantization scheme, it produces an operator F(W), while in the BJ scheme, an operator F(BJ). The Wigner transform of F(BJ) is g, while that of F(W) is f (because it was constructed through its inverse). The inverse-BJ transform of F(BJ) is f, but that of F(W) is yet another function, k. In general, f does not contain ħ, but g does, and likewise k does. For f the square of the classical angular momentum, both F(W) and F(BJ) are flat wrong--the correct F is found by the "art" mentioned ... consistency, convenience, and experience in fitting data.
So, my likes tend to avoid quantization and focus on the mere representation change. Geometric quantization people, to give them their due, have made recondite progress, and the articles you sent me to set the stage; but I am not expert in such, and I'm not sure they actually have come close to solving that mystery. My "WP eyeballs" expression referred to casual readers of WP seeking quick enlightenment.... Cuzkatzimhut (talk) 22:32, 15 June 2017 (UTC)

## A few questions on units

Hi, thx for your reply, I have a few questions to the subject of strong and weak interaction:

I don't quite get the difference of g (coupling constant), g (coupling strenght), g (coupling parameter), g (colour charge), g (gauge coupling parameter), g'(???). The equations I read seem contradictory to my understanding.

For myself I use different notations for every quantity: ${\displaystyle \alpha _{0}=e^{2}/qP^{2}=0.0072973525664,\alpha _{s}=g_{s}^{2}/qP^{2},\alpha _{w}=g_{w}^{2}/qP^{2}=0.03156,\alpha _{G}=m_{p}^{2}/mP^{2}=5.904997844e-39,}$ ${\displaystyle \alpha _{g}=m_{e}^{2}/mP^{2}=1.7518e-45,g_{s}={\sqrt {\alpha _{s}}}qP=1.8755459e-18C,}$ ${\displaystyle g_{em}={\sqrt {4\alpha _{0}\pi }}=0.30282212,g_{w}=e/sw=3.398135e-19C,g_{se}=??,g_{we}=??=1.730406e-13}$

Please could you explain if g(charge) has units of Coulomb or isn't it rather a different dimension (colour charge)? g' should be the weak charge (??) which is usually denoted Y_W, but I found: g'=Y_W*e, which makes units of Coulomb. Ra-raisch (talk) 17:53, 2 August 2017 (UTC)

In high energy physics and QFT, all couplings g are dimensionless, as they are all in natural units in the Lorentz-Heaviside rationalized branch thereof. You may convert them to Coulombs or anything you prefer, to talk to engineers, for instance here, so e ~ 0.303 amounts to about 1.602 ${\displaystyle \cdot 10^{-19}}$ Coulombs and so on... So the weak couplings g are related to this one by division by the sine of the standard Weinberg_angle, and the strong coupling (color charge) also called g_s, but clearly distinguishable from context, is about 1 at the confinement radius.
The only silly usage above, to be avoided!!, is "coupling constant", since they are all variable couplings dependent on the scale: that's what the β function maps out. All other names are basically equivalent. A good QFT text would help you out, or a dozen WP articles on these subjects, but this is not a forum. Cuzkatzimhut (talk) 19:13, 2 August 2017 (UTC)
thanks again, the running of these "constants" is well known, also the value of e=1,6021766208e-19 C and also sw=sin.the_w even within codata giving different values from sw=²(1-m_W²/m_Z²)=0.47212 and sw=²(0,2223)=0,471487 and sw=sin.the_w=sin.28,13°=0,427626 .... sorry I'm using commata for decimal points.
You may convert them to Coulombs or anything you prefer, I didn't intend to transfer colour charge or other quantities to a fantasy unit if it isn't loaded with Coulombs.... Ra-raisch (talk) 20:52, 2 August 2017 (UTC)
OK, then, are we on the same page? As dimensionless numbers, e ~0.30 ~ g × 0.43 , and g_s ~ 1.221 at the mass of the Z boson. As a routine practice, I'd go to the PDG site to get the latest detailed numbers... So there is no question/doubt left, no? Cuzkatzimhut (talk) 21:47, 2 August 2017 (UTC)
not quite yet, dimensionless numbers are very good as long as I know where they come from. e/qP=0.0854 ist good but e/mP=7.361e-12 is completely different ... α=1/137 derives from e²/qP² which denotes the em.strength just like (αg=me²/mP²=1,7518e-45 and) αG=mp²/mP²=5,904997844e-39 denote the grav.strength. But where does g or g' come from? There is no weak or strong charge measurable, only the count of units is known. Of course it is sufficient to compare forces directly, is that possible with weak or strong interaction?
I like to have the dimensions clear, a mass of "1" is not the same as a length of "1" with dimensional denominations there can be no doubt. So I guess, that colour charge is a different dimension (property of matter or spacetime) to time s, volume m³, mass kg and el.charge C or their combinations. At first, the size of a unit in a new dimension may be declared freely, of course. Why not name the unit of colour charge "cc". I understand that physicists are too afraid of declaring a new dimension not experienced in our macro world, still colour charge might be understood as a property derived from our known dimensions some day, like magnetisme is based on moving el.charges... Ra-raisch (talk) 09:27, 3 August 2017 (UTC)
Sorry, I still don't know whether you are asking a question on metrology, in which case Nondimensionalization should answer it, or a question on physics. Through a long sequence of experiments in particle physics, people have measured an enormous number of quantities that depend on the strong (color) , weak, and electromagnetic interaction couplings, as computed and well-understood. These quantities can be cross sections, lifetimes, energy differences, etc... You may think of them as energies and forces, as in classical electromagnetism, if it makes you feel more conceptually secure.) At the end of the day, they are all dimensional consistent. The dimensions of these charges are al dependent, i.e. these charges can be measured in terms of fundamental physics constants, here ℏ, c, etc... So, in HEP, a coulomb, a stat coulomb, etc.. are unfortunate historical engineering units, as Nature provides more convenient definitions from them. As long as you are happy with the conversion factors, you may unambiguously define any and all units you'd like---but there is no physics, or meaning in them, beyond chained definitions of equivalences. In HEP, people use natural units, (almost! they still use the eV for energy!) . Strong and weak forces energy splits, etc... are as real (if not more !) as their electromagnetic analogs. But the is physics and you must read up on the suitable texts to get a glimpse. This is a very poor value for introductory HEP... Cuzkatzimhut (talk) 10:45, 3 August 2017 (UTC)
I don't worry about h°, e, eV, natural units, atomic units or whatever as a unit, what I am worried about is leaving the units away. And even more, leaving the conversion factors away! Maybe you know that a rocket (Mars Climate Orbiter) got lost because of mixing up metric measures with lbf ... Also measuring the forces or energy gives similar results for magnetisme or gravitation though the source is completely different, so it does not say much about the origin of strong or weak forces to measure the reactions. Of course since weak and strong forces are only active in QCD and QFD, this seems not so urging, I guess GUT and TOE is aming at this question though. Ra-raisch (talk) 11:20, 3 August 2017 (UTC)
Well, that's just it! Nobody is "leaving the units away" in nondimensionalization. In natural units, ${\displaystyle e^{2}=4\pi \cdot 0.007(\hbar c)}$, and the units in the parenthesis are implied, since everybody in the field knows they are there from elementary dimensional analysis. It cannot lead to confusion, if one does the conversion consistently and correctly. Nobody would berate you if you keep on writing extra superfluous ℏ, cs in all expressions, as long as you appreciate their numbers and powers cannot be different than the canonical values, or else you've made a bad mistake! If you trust the text, though, there is zero information beyond dimensional consistency in writing them down. In interfacing with engineering, you insert the unique correct number of ℏ s and c s, convert them into your favorite engineering units (state them so as not to get the NASA fools confused) and measure/design.
But you appear to be in confusion about the "nature" of the dimensionless coefficients of these units, so dimensionless e, g, g_s... They are coupling coefficients in different formulas dealing with different physical quantities, electric charge, weak charge, hypercharge, color, etc... what varies in these formulas is the species and interactions, not the units. They don't need different units any more than you need "horizontal meters" versus "vertical meters" in civil engineering! Cuzkatzimhut (talk) 13:20, 3 August 2017 (UTC)
I'd say natural units (in any variant) isn't a system of units. It is just clever notation. (Dimensionful natural units is a different thing entirely, like Planck units.) YohanN7 (talk) 14:16, 3 August 2017 (UTC)
I think, it's ok in the field, I think, it's not so good in wiki though, especially since SI is an international convention. The problem is often on top, that it isn't clear at all, what kind of unit the result is meant to be. Ra-raisch (talk) 18:29, 3 August 2017 (UTC)
I (over)emphasized this in Beta function (physics) as per your suggestion. But explaining natural units again by inserting a parenthesis like so: α = e2/4π(ℏc), and reminding the reader to drop the parenthesis as implied, would only confuse matters. The point is, at the end of the day, one parlays the different orders in the perturbative series for a function of genuinely dimensionless α s. Essentially, this is a highly technical stub that should pretend to be a tutorial of the renormalization group, but, instead, a quick informer stub. Cuzkatzimhut (talk) 21:49, 3 August 2017 (UTC)

## About the intuitive geometric significance of Split-complex number and Pauli matrices in a plane.

About the intuitive geometric significances of Split-complex number and Pauli matrices in a plane. I think it is worthy to add them. Would you please think about it? Lily Lily (talk) 12:47, 23 October 2017 (UTC)

Hi User:Lily Lily, welcome to Wikipedia. I'm afraid you misunderstand the system. "Discuss" refers to that article's Talk page, not mine. Your implicit proposal has little to do with what I, personally, think--I am not the "gatekeeper". You must detail your proposed additions, in good English, in the article's Talk page, and pass muster with the large number of its page editors, whom you should address: you are arguing to a group. In my view, even if the remark were appropriate, it should be a formal footnote near the end of the article, and certainly not in the Lede! In my view, the place where this remark might have a place is the article on Quaternions. In any case, the off-the-mainstream e-print archive reference argues against it, and, in addition, the non-intuitive nature of the proposal, unsuitable for an inexpert audience and students. You might even expound on it in length on your own Talk page, where technical talk need not be inappropriate. However, so far, it appears you are a single purpose user, merely dedicated to promoting a marginal reference in Wikipedia.Cuzkatzimhut (talk) 13:35, 23 October 2017 (UTC)

## Why deprecate TeX?

You reverted one of my recent edits, with edit summary:

(Reverted good faith edits by Yahya Abdal-Aziz (talk): Conversion to inline TeX deprecated, due to platform inflexibility: be considerate to other users! (TW))

I don't understand what the problem is. My edit used markup similar to that already in use in that article to present several variables and functions more self-consistently, and that was motivated by being "considerate to other users!" Many readers fail to connect two occurrences of the same entity when they're presented in different typefaces or styles, and that's what I thought I was fixing.

Is it simply that some hardware devices and software platforms don't understand the markup we use? And if so, surely we're not writing for the lowest common denominator hardware and software imaginable, e.g. an Apple II, TRS-80 or Commodore 4!

Earlier on your talk page I noticed a long history of discussion (and confusion!) over using Tex. Could you please point me to a concise statement, whether in Wikipedia policies, guidelines or even essays, that will clarify:

1. What markup is preferred (e.g. if not TeX then MathML or MathJax or …); and
2. Why?

Thanks for your attention! yoyo (talk) 02:50, 9 December 2017 (UTC)

Indeed, item 7 above touches upon the issue. Displayed eqns should , of course be in TeX. But, by experimenting with several display choices in your Preferences, you can see that inline TeX can be a terrible idea for several platforms, devices, printers, and systems. Explore the ransom letter effect. It is not only "Commodores" who suffer from inline TeX. WP has developed its math templates to address these problems and you are more than welcome to use them. I certainly accept your good faith. Eventually MathJax will triumph, but we are not there yet.... See Wikipedia:Rendering_math. Cuzkatzimhut (talk) 03:17, 9 December 2017 (UTC)
In any case, Wikipedia:Manual of Style/Mathematics # Typesetting of mathematical formulae states "Large scale formatting changes to an article or group of articles are likely to be controversial. One should not change formatting boldly from LaTeX to HTML, nor from non-LaTeX to LaTeX without a clear improvement. Proposed changes should generally be discussed on the talk page of the article before implementation. If there will be no positive response, or if planned changes affect more than one article, consider notifying an appropriate Wikiproject, such as WP:WikiProject Mathematics for mathematical articles." Cuzkatzimhut (talk) 20:59, 11 January 2018 (UTC)

## Philosophical involution

Hi, long time no see! I also -luckily- did not encounter that Prokariotes since then. ;)

I'm just here to report that, while wading through disambiguations, I perceived some urge not to select the mathematical article about involuting something, but the philosophical one, instead. I cannot precisely recall my motivation to do so, but for now I want to thank you for your correction. Please, assume I know about the mathy meaning of involution, too. In case some convincing argument for philosophy overcomes me, I'll leave an extensive edit summary. :)

With the best seasonal wishes, Purgy (talk) 14:15, 1 January 2018 (UTC)

Best wishes too; yes, compelling philosophical hankerings can make conceptual dust bunnies of all of us....Cuzkatzimhut (talk) 14:28, 1 January 2018 (UTC)

## Hermite Polynomials

Section transfered to footnote: much better in my opinion. Thanks for compromising. Herbmuell (talk) 16:07, 19 January 2018 (UTC)

You are welcome. My experience is that anyone visiting this article is not a clueless undergraduate. I've grown to appreciate that an increasing number of advanced undergraduates, graduate students, and up, by now even rely on WP to map out the territory: "what is there available?". They don't always go for depth. In that sense, the fractional and continuous Fourier transform and Mehler kernel handles should allow them to access the Wiener picture, if interested... Cuzkatzimhut (talk) 17:29, 19 January 2018 (UTC)