Talk:Gauge theory

This page vs. Introduction to gauge theory

Why is there a separate Introduction to gauge theory page? Shouldn't an encyclopedia article be an introduction to a subject? It seems like it'd be better to combine them into a single page, or split this main article out into more specific technical pages and replace it with the introduction. — Preceding unsigned comment added by 2601:647:4D03:3CA7:A860:47C9:1D45:B8DD (talk) 10:34, 15 June 2017 (UTC)

   The first sentence is a great example of how Physics articles on Wikipedia can be utterly incomprehensible. The first sentence of this article: "In physics, a gauge theory is a type of field theory in which the Lagrangian is invariant under certain Lie groups of local transformations." contains four terms I don't understand: "field theory", "Lagrangian", "Lie groups", "local transformations". I guess I could read up on those terms on their respective pages. Let's take "Lie groups", the first sentence of that article is: "In mathematics, a Lie group is a group that is also a differentiable manifold, with the property that the group operations are compatible with the smooth structure." Three terms I don't understand: "Differential manifold", "group operations", "smooth structure". It just keeps branching out! How can an uninformed reader ever grasp what is being said? 

Although I applaud the creation of the Introduction to gauge theory page, I completely agree with the above comment: encyclopedia articles should be an introduction to a subject. 217.76.25.109 (talk) 22:11, 19 July 2017 (UTC)

This would be very difficult, but I'll see if I can come up with something when I have time. So far, here are the issues:

* We could improve the description of the Lie group article to be more familiar to non-mathematicians who use it for other purposes (your average physicist would have trouble fully understanding that introduction). I think knowing what is a Lie group is important to understanding this; although one could give a rough idea of it just by using the term "infinitesimal local transformation" and ignoring Lie groups. (see below for more elaboration on this)

* Field theories are just physical theories about fields; like how fields evolve over time, interact with each other, etc? Quantum field theory and classical field theory are so structurally different that it's hard to say "X is precisely and exactly what a field theory is", so explaining that further will get people to argue over the definition of words. Usually field theories are quickly summarized in this function called a "Lagrangian". I don't think Lagrangians are strictly necessary for a gauge theory (I'm not sure about this, can someone verify?), but all the treatments of gauge theories that I have ever seen use Lagrangians.

* "local transformation" in this context is simultaneously not notable enough to merit its own article, but also kind of hard to define on its own. Essentially, we want too say that if we have a (vector field) $f(x)$, a local transformation takes $f(x)$ to $g(f(x))$ for some (typically linear) function from the vector space to itself $g$, as opposed to a transformation that takes $f(x)$ to $f(x+a)$ for example. Essentially, we want the transformed field at x to only depend on the original field at x. (erm, does that work/make sense?)

If we want to make this article more comprehensible, we could add a section starting with a simple introduction; in fact the article titled Gauge Fixing gives a very intuitive but also kind of badly written introduction to this. We could also be like the math pages and define terms like "gauge" (a basis for our vector space at any particular point), and define everything clearly enough so that it becomes understandable? (but then we would have to link fibre bundles and whatnot to make the mathematicians happy) Physics undergraduates don't touch gauge theories until they do their Ph.Ds (so, for some of them, it's just "never"), so this is difficult to explain in a simple way that is also correct. Qwyxivi (talk) 03:25, 28 September 2019 (UTC)

Not so difficult, anything that is PhD-level only can safely be removed from the encyclopedia.134.160.214.17 (talk) 08:18, 9 March 2020 (UTC)

84.114.240.91 (talk) 14:40, 21 June 2020 (UTC) The subject is very difficult, indeed. To help at least physics students with just basic (BS) knowledge to get a grip on it, I added a link into the "external links" section to here: https://www.goldsilberglitzer.at/Rezepte/Rezept008E.pdf. It explains it without "Lie groups", "Lagrangian", etc. However, the link was immediately removed. Maybe this decision should be re-considered. — Preceding unsigned comment added by 84.114.240.91 (talk) 14:33, 21 June 2020 (UTC)

The pdf is just a non peer-reviewed blog of conventional material on electromagnetism already in Wikipedia. Do you have any COI in the matter? Xxanthippe (talk) 22:34, 21 June 2020 (UTC).

84.114.240.91 (talk) 20:35, 27 June 2020 (UTC) Sorry, I don't quite understand. The pdf is not about "electomagetism". It is exactly about gauge theory, and it demonstrates how - starting from the Schrödinger equation (basic quantum theory) - Gauge theory "magically" produces the electric and magnetic field - which is the core of Gauge theory. Also, I was not able to find such a basic and yet complete demostration elswhere (esp. not on Wikipedia). But you are right, of course, when saying that it is not peer-reviewed. What is COI? Conflict of interest?

"under certain"

In physics, a gauge theory is a type of field theory in which the Lagrangian is invariant under certain Lie groups of local transformations.

Under certain wider range transformations we have dark matter and Roger Penrose's Big Bang (suddenly, after an energy threshold overflow of an extremely old expanding universe, that Universe is caught by police, and the only way to make its Lagrangian invariant again is to implode).

Under certain allows room for new theories. — Preceding unsigned comment added by 2A02:587:411C:3400:6121:B908:16E1:BD7 (talk) 03:44, 12 July 2018 (UTC)

Pronunciation

Should have something on the pronunciation of the word "gauge", which is unexpected based on the spelling... AnonMoos (talk) 20:46, 27 July 2021 (UTC)

Apostrophes for comparative variables

I think the section containing

$\ \Phi \mapsto \Phi '=G\Phi$

and the following sections could be made clearer by avoiding apostrophes when there is also talk of derivatives. Or at least specifying what the primed version is intended to mean. Haukurb-dev (talk) 11:41, 27 July 2023 (UTC)

Gauge definition

This article refers to a gauge as "any specific mathematical formalism to regulate redundant degrees of freedom in the Lagrangian of a physical system."

However, in the article Gauge fixing#Gauge freedom, a gauge is referred to as "A particular choice of the scalar and vector potentials". This definition makes more sense to me, as when you, for example, perform a gauge transform, it is these potentials which undergo the transform, not the mathematical formalism which undergoes the transform. 2001:67C:10EC:2886:8000:0:0:FE (talk) 18:38, 2 May 2024 (UTC)

Then again, in the gauge fixing article they go on to say that a more precise term for their definition is a "gauge potential", so I am not sure if the term "gauge" by itself refers to something different than the gauge potentials. 195.176.96.210 (talk) 18:43, 2 May 2024 (UTC)