# Talk:Gauge theory

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The history of this article may be a little confusing, so I'll give a brief explanation. There was a long discussion, archived above, about problems with accessibility to the general reader. In August 2009, I spun off the technical stuff into Mathematical formalism of gauge theory, leaving the nontechnical material in Gauge theory. Bakken then renamed the articles so that that Gauge theory was the technical article, with Nontechnical introduction to gauge theory being the nontechnical stuff. Confusingly, the old edit history of Gauge theory is now all at in the edit history of Nontechnical introduction to gauge theory.--76.167.77.165 (talk) 15:28, 10 August 2009 (UTC)

People seem to think that Gauge Theory is difficult. Bah! What's really confusing is the history of this article;) YohanN7 (talk) 22:45, 15 October 2009 (UTC)

Haven't the histories been merged here already? The history of Nontechnical introduction to gauge theory is basically empty now and this page's history seems coherent and complete. So, shouldn't the {{copied}} template be deleted from this talk page? — Pt(T) 20:50, 21 February 2010 (UTC)
Nontechnical introduction to gauge theory was subsequently renamed to Introduction to gauge theory, and the history of that page is where all the pre-2009 activity for the Gauge theory article can be found. –Henning Makholm (talk) 21:50, 29 September 2010 (UTC)

Could the red link "Gauge transform" be replaced by the green link "gauge tranformation"? Puzl bustr (talk) 21:13, 13 September 2009 (UTC)

(This used to be in the middle of the above discussion, but it clearly is a separate comment. As of this writing, the redlink that existed in September 2009 has indeed been replaced as suggested by Puzl bustr. –Henning Makholm (talk) 22:02, 29 September 2010 (UTC))

## Merger Proposal

I don't think we can write much about Gauge symmetry that can't be included in the general article about Gauge theory
SPat talk 03:55, 31 October 2009 (UTC)

## Gauge Transformation

Could somebody explain why the current gauge transformation formula ${\displaystyle A'_{\mu }=GA_{\mu }G^{-1}-{\frac {1}{g}}[\partial _{\mu },G]G^{-1}}$ is better? The formula without a commutator seemed perfectly correct to me (I'm talking about the last change). Terminus0 (talk) 21:43, 29 November 2009 (UTC)

It amounts to the same thing, but I agree that the former expression was less confusing. --Michael C. Price talk 23:49, 29 November 2009 (UTC)
It's not clear to me that it amounts to the same thing; there's an extra factor of 2. I understand the commutator notation to mean ${\displaystyle [\partial ,G]G^{-1}=(\partial G-G\partial )G^{-1}=(\partial G)G^{-1}-G\partial G^{-1}=2(\partial G)G^{-1}}$ (last equals due to ${\displaystyle 0=\partial I=\partial (GG^{-1})=(\partial G)G^{-1}+G\partial G^{-1}}$). I have changed it back to the commutator-less notation, which is correct according to my rederivation –Henning Makholm (talk) 22:45, 29 September 2010 (UTC)
Argh, scratch that! I was trying to evaluate the commutator between things of different rank (understanding ${\displaystyle G}$ as an n×n matrix and ${\displaystyle \partial }$ as an operator on such matrices), which Is Not Allowed. It is indeed true that
${\displaystyle [\partial _{\mu }^{n},G]G^{-1}=(\partial _{\mu }^{n\times n}G)G^{-1}}$
where ${\displaystyle \partial _{\mu }^{n}}$ is a differential operator on n-vectors, the commutator is computed in the ring of linear operators on n-vector fields, and ${\displaystyle \partial _{\mu }^{n\times n}}$ is a differential operator on n×n matrices. It is also true that
${\displaystyle [\partial _{\mu }^{n\times n},G{-}](G^{-1})=(\partial _{\mu }^{n\times n}G)G^{-1}}$
where the commutator is an operator on n×n matrices which operates on ${\displaystyle G^{-1}}$, and ${\displaystyle G{-}}$ denotes left multiplication by ${\displaystyle G}$. But either of these readings is too subtle to expect a random reader of the article to figure out, especially given that they don't seem to be more useful than the right-hand side. –Henning Makholm (talk) 03:06, 10 October 2010 (UTC)

## Pure gauge

The section Gauge theory#Pure gauge was merged here from Pure gauge in November 2008 with no discussion, having been a separate article before. However, it doesn't really seem to belong here, being a brief snippet on a too specialized subtopic. Perhaps move it into Gauge fixing? Or write more on it (well, that should anyway be done) and promote it into a separate article again? Currently its importance is not anyhow evident.  Pt (T) 12:25, 20 December 2009 (UTC)

## Quantum gauge theory: expand or merge?

The section Gauge theory#Quantization of gauge theories should link to Quantum gauge theory as the main article. Right now the link is only amidst the "See also" section and in a general template. However, there is nothing to link to! The Quantum gauge theory page has truly nothing to add the present section in this article nor the quantization page. So I'd encourage a complete rewrite of Quantum gauge theory to systematize and summarize the many methods. If that is deemed unnecessary, the page should rather be merged here.  Pt (T) 04:48, 22 December 2009 (UTC)

I've now added the link. It does no harm, at least… But the sad situation with Quantum gauge theory has not yet improved anyhow. — Pt(T) 05:59, 3 September 2012 (UTC)

## Definition

What about global gauge invariance? —Preceding unsigned comment added by Paranoidhuman (talkcontribs) 22:15, 17 March 2010 (UTC)

## Order of sections

I swapped the order of the sections to place the more general "Description" of gauge theories, before the specific mathematical examples in "Classical gauge theory". I found the transition in level of description be jarring when read in the original order.

I don't think that this breaks any topical dependencies. Eric Drexler (talk) 03:06, 17 May 2010 (UTC)

## Removal of the cleanup tag

I've removed the cleanup tag that had been on the page since last August. In between, much of the article has been reworded, the old complaints are mostly yet older than the tag was and, in my humble opinion, are not directly applicable anymore. There are no specific active cleanup proposals on the current talk page. If you feel there is still any need for such a prominent tag, then feel free to put it back, of course! — Pt(T) 21:25, 4 June 2010 (UTC)

## Is the gauge really a function?

in this edit, an anonymous editor added:

A gauge is a function introduced into a field equation to produce a convenient form of the equation but having no observable physical consequences. The transformations between possible gauges (called gauge transformations) must form a Lie group...

In my understanding, specifying a gauge means adding another equation to accompany the field equation(s). Thus, the gauge is an equation and not a function. E. g. the Lorenz gauge is ${\displaystyle \partial _{\mu }A^{\mu }=0}$. Another viewpoint often employed is adding a gauge fixing term to the lagrangian (see ${\displaystyle R_{\xi }}$ gauges in particular), calling the term a function would be a very loose use of the word (a function from where to where?). Its effect on the field equations is not as trivial as "just adding a function", it rather follows the idea of lagrange multipliers. — Pt(T) 14:26, 2 July 2010 (UTC)

I agree with you. Have just rephrased the sentence. Bakken (talk) 16:15, 3 July 2010 (UTC)

## Gauge Symmetry

The page on Gauge Symmetry is unreadable and should just be deleted with a comment -- see gauge theory. — Preceding unsigned comment added by Stevesimon2 (talkcontribs) 16:00, 24 July 2011 (UTC)

## Pronouniciation

Can we have one of those pronunciation guides, please? — Preceding unsigned comment added by 82.41.201.163 (talk) 11:15, 23 November 2011 (UTC)

## Gauge Invariant

There is no explanation of "Gauge Invariant", even though the article on "Gauge Invariant" redirects here. — Preceding unsigned comment added by 173.13.158.102 (talk) 23:26, 18 December 2011 (UTC)

## Global/Local Symmetry

Why is it said that local symmetry is a stricter constraint? To me, in the usual mathematical notion of strict or weak, local symmetry is a weaker notion than global symmetry--and hence more general--by simple virtue of the fact that global symmetry implies local symmetry whereas the other direction is false in general. — Preceding unsigned comment added by 66.213.36.2 (talk) 18:22, 13 March 2012 (UTC)

## An example: Scalar O(n) gauge theory

Shouldn't it read (change in bold):

The gauge field is an element of the Lie algebra, and can therefore be expanded as
${\displaystyle \ A_{\mu }=\sum _{a}A_{\mu }^{a}T^{a}}$
There are therefore as many linearly independent gauge fields as there are generators of the Lie algebra. — Preceding unsigned comment added by Dieterich (talkcontribs) 14:15, 16 April 2012 (UTC)

## Mathematical Language

This article is clearly written by a physicist. While the author tries to translate some of it from physics to math (and it is much appreciated), there are a lot of translating errors. I would change them myself, but no one seems to like my edits. — Preceding unsigned comment added by K3thomps (talkcontribs) 16:24, 19 June 2012 (UTC)

Hi K3thomps, I understand your point about inaccurate language, please feel free to change wherever you think you can make improvements. There shouldn't be any problem as long as all content is verifiable. If you need any help with finding or added references, let me know. Remember, Be Bold!
SPat talk 18:30, 19 June 2012 (UTC)

## Mathematical Language Again

The section Gauge theory#Mathematical Formalism needs to build a bridge between the physicists and the mathematicians formulation of Gauge Theory. It doesn't do that.

For example, the section begins with "... Mathematically, a gauge is just a choice of a (local) section of some principal bundle...". Exactly how does this relate to the (excellent) examples given earlier? Specifically, how does the examples constitute the ingredients of a principal bundle? What are the manifolds involved? What are the maps between them? Etcetera, etcetera ...

Where do things live?

Please make this section relate to the rest of the article. I am sure that the whole article would benifit enormously. YohanN7 (talk) 08:23, 21 August 2012 (UTC)

WP:SOFIXIT?

## The 2012-10-10 edit

I'm not sure the edit is helpful. For one thing, it's not clear that local gauge invariance is stricter than global gauge invariance. I'd say it's the other way around. Also, while Lagrangians are central objects in practice, they are perhaps not of foundational nature in quantum field theory (see e.g. weinberg, QFT vol 1). I don't say the edit is bad, just that I'm not sure, especially when it comes to the stricness part. YohanN7 (talk) 13:54, 11 October 2012 (UTC)

Since any Lagrangian with local gauge invariance also has global gauge invariance (assuming that spacetime is topologically trivial so that there are no topological shenanigans), the class of Lagrangians with local gauge invariance is strictly smaller than the class of Lagrangians with global gauge invariance.TR 06:50, 12 October 2012 (UTC)

## The meaning of "gauge"

The word "gauge" has many meanings. What does it mean as it appears in "gauge theory"? Is it "[measure] theory", or "[measuring] theory" or "[thickness] theory" etc? — Preceding unsigned comment added by 144.122.104.211 (talk) 20:15, 29 May 2013 (UTC)

## O(n) Result Changed

I believe there was an erroneous misplacement of factors of i when calculating the interaction Lagrangian found at the end of the O(n) gauge theory section. I changed it but would appreciate someone checking this as well, and perhaps even finding a reference who completes the calculation independently. Brent Perreault (talk) 20:47, 30 October 2013 (UTC)

## Local symmetry group

Should Local symmetry group link here? 70.247.161.12 (talk) 14:11, 28 April 2014 (UTC)

## section "2.1 Global and local symmetries"

How is that an appropriate title for this section? At no point does this section make the slightest attempt to define what a global or local symmetry is, or what the difference is between them. In fact, neither the word "global" nor the word "local" ever appears in it, except to say that the idea can be generalised to include local as well as global symmetries. Quite what that's actually supposed to mean is left entirely unclear. — Preceding unsigned comment added by 131.169.205.156 (talk) 15:34, 2 February 2015 (UTC)

## section "2.2 Gauge Fields"

This needs to be rewritten. You cannot begin the first paragraph of a new section using vague pronouns instead of specific subjects. The topic is confusing enough, there's no reason to make the text indecipherable. "The "gauge covariant" version of a gauge theory accounts for this effect by..." What effect? Michael McGinnis (talk) 21:50, 15 September 2016 (UTC)