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Differential form of the path integral
I find the statement "He expressed the Feynman path integral in differential form" to be misleading in the sense that it implies that Schwinger started with the path integral and rewrote it in differential form. However this is not at all the case. Rather Schwinger's differential formulation of QFT was later found (by Dyson) to be equivalent to Feynman's path integral approach. Ty8inf (talk) 03:51, 2 November 2009 (UTC)
- In fact, it is exactly true that Schwinger started with the path integral and rewrote it in differential form. To clarify: the thing that Dyson did is to show that the Feynman diagrams (not the path integral) could be derived from the standard time-dependent perturbation theory. This is not a surprise, in hindsight, because the time-dependent perturbation theory is just the form that the path-integral takes when you work with an "integral" over transitions between discrete energy levels. But dyson explicitly showed that Schwinger's equations of motion and the perturbation series that he used would come out of time dependent perturbation theory, which was a standard tool. This allowed physicists to learn Feynman diagram methods without using the path integral. That was historically important for the acceptance of the new methods, but it has nothing directly to do with the Schwinger variational principle.
- What Schwinger was after was something altogether different. He wasn't trying to formulate diagrams, he wanted the equations of motion and canonical commutation relations for fields to come from an obviously relativistically invariant Lagrangian formulation. Feynman had completely solved the problem for bosonic fields--- the path integral is the answer--- but he couldn't handle Fermions the same way. When Feynman dealt with Fermions, he formulated their theory with diagrams for the particle paths, but didn't give a path-integral for their fields.
- The reason is that the theory of the path-integral of Fermionic fields required a mathematical innovation, called Grassman integration. Grassman variables and Grassman integration were invented in the 1956 by David John Candlin in the west, and by Felix Berezin in the east a little later. Both started from the known Feynman diagram expansion for Fermi fields, and developed the same formalism. Berezin went farther with it then Candlin, but Candlin came first.
- Anyway, Schwinger's action principle predated both Candlin and Berezin. Schwinger didn't know how to integrate over Fermionic fields, so he decided that it wasn't necessary to integrate at all！ His idea was to replace the integral in the path-integral by a set of differential identities which would be equivalent to the path integral, and could replace it. The idea was to consider a Lagrangian with extra source terms coupled to different operators, and then to differentiate with respect to the sources. This would pull down different operators in the integral. Then you could make rules for how the derivatives of the path integral behaved without dealing with the integral itself. This formal trick allowed Schwinger to recast the path-integral as a set of differential identities which include the equations of motion for the operators and the commutation relations.
- Schwinger could easily do this for bosonic fields, because of the path integral. After he dealt with bosons, he found that the same formal rules worked without any problem in the case of Fermionic fields too. This was a surprise, and for this reason (I think) he suggested that the differential form of the action principle is more fundamental than the path integral. The reason, in hindsight, is because there is a consistent fermionic integration, but Schwinger didn't know that. The formalism Schwinger used was the first Lagrangian formulation which could deal with Fermions and Bosons on equal footing. Feynman felt uncomfortable with path-integrals well into the sixties because he was not sure how to deal with Fermions. A lot of other people did too. Path integrals only became mainstream in the 1970s, as Grassman integration became a standard part of the physicists toolkit.
- Schwinger disguised the path-integral origin of the action principle to some extent. Maybe it was the rivalry with Feynman, maybe it was because he felt that the path integral was only heuristic (a lot of people felt that way back then), or maybe he felt that a quantum mechanical formalism that didn't allow for Fermionic fields was essentially incomplete. I don't know the reason. But the Schwinger variational principle is historically important because it did allow many people to do something equivalent to Grassman integration before Grassman integration was defined.Likebox (talk) 05:12, 19 January 2010 (UTC)
Schwinger's Quote Regarding Feynman
About this quote:
"Like the silicon chips of more recent years, the Feynman diagram was bringing computation to the masses."
I am reminded of a quote attributed to Newton about how he (Newton) stood tall merely because he stood on the shoulders of giants. Most of the time, that quote is used to imply a humility on Newton's part; that implication, however, is incorrect. Newton was actually referring to a rival of his (a German, I believe) who was known for his physically short stature.
I mention this because James Gleick in Genius states explicitly that Schwinger was being anything but respectful with that line; that in fact that he (Schwinger) considered it pedagogical tool, not a scientific tool. I believe that another line should be added to emphasize this point.
--NBahn (talk) 03:55, 25 July 2010 (UTC)
- You are of course referring to Leibniz who was involved in a bitter dispute about which had invented differential calculus.
- The article Standing on the shoulders of giants says the phrase has been documented in use before Newton.
- The article Standing on the shoulders of giants says Newton clearly used the phrase referring to his own work and not to Leibniz.
Immigrate versus migrate
Hi, I think there is a misunderstanding at work here. The term to "immigrate" is used in relation to a country to mean that a person relocates to that country. To "emigrate" is used in relation to a country to mean that someone leaves that country. Therefore, no matter from which perspective it is viewed, the term is clear for international readers, and the meaning of the sentence is that the person moved to the US from another place. Moreover, to "migrate" does not have the exact same meaning, and, while it not wrong to use the term, it is less precise in this situation. Silvrous Talk 10:13, 23 February 2013 (UTC)
Yes, there is a misunderstanding at work here - and I think it is you who are misunderstanding. One action of relocating one's life from Poland to the US can be described with 3 variants of the same verb
The only distinction between the verbs is that 'Emigrate' implies the country from which they departed according to the implied location of the author, 'Immigrate' implies the country in which they arrived again according to the implied location of the author and 'Migrate' makes no implication as to the perspective of the author, requiring origin and destination to be specified explicitly. The implications of author location translate into assumptions that the readers share the same location as the author
There is indeed a tautology in saying "immigrated to America" for US readers, because America is stated once and implied once, although this is consistent for those readers. This is a jarring contradiction for readers from all other locations because their own location is implied, but America is stated. The jarring conflict is only resolved by concluding that the author is based in the US. I note that you rejected the alternative "emigrated to America", which would be consistent for Polish readers, because Poland is both stated and implied but jarring for readers from all other locations unless they conclude that the author is based in Poland,
As I understand it, Wikipedia is neutral in author perspective - articles are not written from a US perspective and should strive to avoid this. That being the case 'migrate' is the correct word to use to preserve that neutral perspective. 'Alternately' (for users of US English and 'Altenatively' for users of UK English), if you insist on using the 'word 'Immigrate', it has to read:
Julian Seymour Schwinger was born in New York City, to Polish Jewish parents Belle (Rosenfeld) and Benjamin Schwinger, a garment manufacturer, who had 'immigrated' (for US located readers, 'emigrated' for readers located in Poland and 'migrated' for all other readers) to America.
Please show some respect for non US users. The verbs 'Emigrate' and 'Immigrate' both imply author location and assume reader location, forcing readers from any other location to evaluate location unnecessarily. 'Migrate' reads equally well for all readers and rightly retains focus on the content rather than extraneous questions of location and perspective. --22.214.171.124 (talk) 11:36, 23 February 2013 (UTC)
Concerning the edit to 'emigrate', this is, of course, a valid way of describing the move made by the Schwinger family for readers based in Poland. In reverting from 'emigrate', user Silvrous states 'As explained on the talk page, it is gramatically incorrect to state that someone emigrates to a country'. This of course is false. Implicit in the context is the fact that the emigration was from Poland and the destination is explicitly specfied as the US. All emigrations and immgrations are from somewhere to somewhere else. There is no grammar error. This is not a syntactic issue, it is semantic. And to portray it as grammatic is a complete misrepresentation of the issue (coming back to this after I have eaten) --126.96.36.199 (talk) 12:52, 23 February 2013 (UTC)
- Oops, apparently I was indeed wrong about the "emigrate to" part. Sorry about that, I'm changing back to your version. Still, I think you are reading too much into the perspective of the reader, there is definitely no "disrespect" to the reader involved in the use of one word. Silvrous Talk 13:29, 23 February 2013 (UTC)
Great! As you are accepting 'emigrate' we have moved on beyond any feeling that articles must be written from a US perspective, However, you have now changed it to a generally European and specifically Polish perspective.
- 'Emigrate' - viewed from the perspective of the origin. By default if no origin specified, this is the perspective of the author, who assumes the same perspective for his readers
- 'Immigrate' - viewed from the perspective of the destination. By default if no destination specified, this is the perspective of the author, who assumes the same perspective for his readers
- 'Migrate' - viewed from a perspective completely outside the move. Origin and destination must be determined by explicit or implicit declaration within the context. Nothing can be inferred or assumed from the location of the author or the reader.
Concise Oxford Dictionary: migrate move from one place (country, town, college, house) to another; ...
I'll admit to trying it on with 'emigrate' - for me it suffers the problem as 'immigrate' in that it imposes a perspective. Given the definition above, from a respected dictionary, can you now accept 'migrate' and eliminate all questions of perspective?--188.8.131.52 (talk) 14:18, 23 February 2013 (UTC)
- You can always change it yourself back ( WP:BOLD ). I looked up other articles, and could only find either "emigrate", such as in Albert Einstein or "immigrate", such as Arnold Schwarzenegger. But I was wrong in the beginning, the words can be used interchangeably with only a difference in nuance, so I guess you could say that they migrated. Silvrous Talk 15:53, 23 February 2013 (UTC)
- I don't even try discussing etymology with English speakers anymore. I always get the answer: "Yes but we've been using this word this way for years. <insert proof by google here> Why should we bother what a word actually meant once?" Evidently people can now push a pedal with their foot "manually", and even NASA can do afocal "projection". I think I'll stick to German and French for scientific precision. :-( --BjKa (talk) 15:13, 10 November 2014 (UTC)
developing a relativistically invariant perturbation theory, and for renormalizing QED to one loop order
This portion is in desperate need of some wikilinks! I find it most unfortunate, that the opening words of any article should be so uncomprehensible to the general public. --BjKa (talk) 15:01, 10 November 2014 (UTC)
Schwinger discovered that neutrinos come in multiple varieties...
I don't think the evidence is that compelling for this statement, but I don't judge myself competent enough to unilaterally edit this out. Supporters of this statement should offer evidence. DMGualtieri (talk) 13:43, 18 December 2014 (UTC)