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Questions tagged [yang-mills]

Yang–Mills theory is a QFT, a gauge theory normally symmetric under a compact non-Abelian Lie group relying on (originally massless) gauge vector fields. YM theories describe the strong and electroweak interactions of elementary particle physics, the Standard Model.

Yang–Mills theory is a QFT, a gauge theory normally symmetric under a compact non-Abelian Lie group relying on (originally massless) gauge vector fields. YM theories describe the strong and electroweak interactions of elementary particle physics, the Standard Model.

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Gravity as a gauge theory

Currently, (classical) gravity (General Relativity) is NOT a gauge theory (at least in the sense of a Yang-Mills theory). Why should "classical" gravity be some (non-trivial or "special" or extended) gauge theory? Should quantum gravity be a gauge…
riemannium
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What does it mean that there is no mathematical proof for confinement?

I see this all the time* that there still doesn't exist a mathematical proof for confinement. What does this really mean and how would a sketch of a proof look like? What I mean by that second question is: what are the steps one needs to prove in…
Physics_maths
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Why is the Yang-Mills gauge group assumed compact and semi-simple?

What is the motivation for including the compactness and semi-simplicity assumptions on the groups that one gauges to obtain Yang-Mills theories? I'd think that these hypotheses lead to physically "nice" theories in some way, but I've never, even…
joshphysics
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Why is the Yang–Mills existence and mass gap problem so fundamental?

Ref: Yang–Mills existence and mass gap Can anyone please explain why the Yang–Mills Existence and Mass Gap problem is so important / fundamental to contemporary mathematics (and, presumably, theoretical / mathematical physics)? If possible, please…
Anonymous
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Which exact solutions of the classical Yang-Mills equations are known?

I'm interested in the pure gauge (no matter fields) case on Minkowski spacetime with simple gauge groups. It would be nice if someone can find a review article discussing all such solutions EDIT: I think these are relevant to the physics of…
Squark
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How to Perform Wick Rotation in the Lagrangian of a Gauge Theory (like QCD)?

I'm studying Lattice QCD and got stuck in understanding the process of going from a Minkowski space-time to an Euclidean space-time. My procedure is the following: I considered the Wick rotation in quantum mechanics $x_0 \to -i x_4$. From this, I…
WilhelmM
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Soliton Moduli Spaces and Homotopy Theory

The four-dimensional $SU(N)$ Yang-Mills Lagrangian is given by $$\mathcal{L}=\frac{1}{2e^2}\mathrm{Tr}F_{\mu\nu}F^{\mu\nu}$$ and gives rise to the Euclidean equations of motion $\mathcal{D}_\mu F^{\mu\nu}=0$ with covariant derivative…
JamalS
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Gauge fields -- why are they traceless hermitian?

A gauge field is introduced in the theory to preserve local gauge invariance. And this field (matrix) is expanded in terms of the generators, which is possible because the gauge field is traceless hermitian. Now why did we choose it as traceless…
Marlin Jar
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Does 4D ${\cal N} = 3$ supersymmetry exist?

Steven Weinberg's book "The Quantum Theory of Fields", volume 3, page 46 gives the following argument against ${\cal N} = 3$ supersymmetry: "For global ${\cal N} = 4$ supersymmetry there is just one supermultiplet ... This is equivalent to the…
Squark
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Yang-Mills CP violation

Why does a term proportional to $\left(F,\,\tilde{F}\right)\propto Tr\left[ F_{\mu\nu}\tilde{F}^{\mu\nu}\right]$ in the Lagrangian of the pure Yang-Mills theory violate CP?
PPR
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Yang-Mills vs Einstein-Hilbert Action

The classical Yang-Mills action is of the form $$S=\frac{1}{2g^2}\int_{\mathcal{M}}\text{tr}\left[F\wedge\star F\right]\\ =\frac{1}{4g^2}\int\mathrm{d}^dx\sqrt{g}\,\text{tr}\left[F^{\mu\nu}F_{\mu\nu}\right],$$ where $F=dA+A\wedge A$ is the…
Bob Knighton
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Spontaneous breaking of Lorentz invariance in gauge theories

I was browsing through the hep-th arXiv and came across this article: Spontaneous Lorentz Violation in Gauge Theories. A. P. Balachandran, S. Vaidya. arXiv:1302.3406 [hep-th]. (Submitted on 14 Feb 2013) The authors say that Lorentz symmetry is…
Sudip Paul
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What is a "free" non-Abelian Yang-Mill's theory?

I hope this question will not be closed down as something completely trivial! I did not think about this question till in recent past I came across papers which seemed to write down pretty much simple looking solutions to "free" Yang-Mill's theory…
Student
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Inverse square rule for strong forces

Most of the forces induced by a point particle follows the $1/r^2$ rule. Then why does the strong force not obey it?
STAIN
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Why is a superposition of vacuum states possible in QCD, but not in electroweak theory?

There are two standard stories floating around in modern particle physics: Spontaneous symmetry breaking can only happen in a QFT, like in the electroweak theory, because no tunneling between the degenerate vacuum states of the scalar field are…
jak
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