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336:* 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.
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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?
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333:* 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)
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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.
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The first sentence is a great example of how
Physics articles on Knowledge 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
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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.
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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
769:, 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.
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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.
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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.
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Also, I was not able to find such a basic and yet complete demostration elswhere (esp. not on
Knowledge). But you are right, of course, when saying that it is not peer-reviewed. What is COI? Conflict of interest?
561:) 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:
339:* "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)
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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.
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This article refers to a gauge as "any specific mathematical formalism to regulate redundant degrees of freedom in the
Lagrangian of a physical system."
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The pdf is just a non peer-reviewed blog of conventional material on electromagnetism already in
Knowledge. Do you have any COI in the matter?
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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?)
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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:
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page, I completely agree with the above comment: encyclopedia articles should be an introduction to a subject.
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Should have something on the pronunciation of the word "gauge", which is unexpected based on the spelling...
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for that content in the latter page, and it must not be deleted as long as the latter page exists.
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on
Knowledge. If you would like to participate, please visit the project page, where you can join
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Not so difficult, anything that is PhD-level only can safely be removed from the encyclopedia.
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In physics, a gauge theory is a type of field theory in which the
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