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6 votes
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Interpretation of self-interacting terms in the expansion of a pure YM Lagrangian?

For what it's worth, if one calculates the symmetric SEM tensor $T^{\mu\nu}$ of the Yang-Mills (YM) theory with a compact gauge group $G$, one may check that the 00-component $T^{00}$ (=the energy-...
Qmechanic's user avatar
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2 votes
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Topological behavior (or asymptotics at infinity) of gauge fields assumed in Fujikawa method

Indeed, from a mathematical standpoint, all the physics that has to do with the global topological terms of gauge theory "on $\mathbb{R}^4$" really happens on $S^4$. So how is it possible ...
ACuriousMind's user avatar
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2 votes

Non-abelian Yang-Mills in 1+1 dimensions

Let us choose the axial gauge $$A_1~=~0.\tag{A}$$ Then the chromo-electric field is $$F_{10}~=~\partial_1A_0-\partial_0A_1+[A_1,A_0]~\stackrel{(A)}{=}~\partial_1A_0.\tag{B}$$ NB: Be aware that $F_{10}...
Qmechanic's user avatar
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2 votes
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Visualization of a gauge field with non-null winding number

The proper answer is that fully visualizing this winding would involve imagining the winding on a 3-sphere. Just in case someone reading this doesn't know why that is, it's because the boundary ...
11zaq's user avatar
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2 votes
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Are Higgs mechanism and SSB different phenomena?

The answer is yes to both your questions. You can have SSB without the Higgs mechanism, but you cannot have the Highs mechanism without SSB. In fact, the Higgs mechanism is the SSB of a (local) gauge ...
LolloBoldo's user avatar
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2 votes

Motivation for pure Yang-Mills Lagrangian

You can look at this from various angles, but the Lagrangean as you write can be (basically) fixed by basic QFT considerations: The $A_\mu^a$ are the basic degrees of freedom of the theory. This the ...
Toffomat's user avatar
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2 votes

Understanding the Gaussian weight and the parameter $\xi$ when quantizing gauge theories

Note that functional integral is independent of the gauge-fixing function $$G~=~\chi-\omega, \qquad \chi~=~d_{\mu}A^{\mu}, \tag{9.55}$$ cf. e.g. this Phys.SE post. In particular it does not actually ...
Qmechanic's user avatar
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1 vote
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Motivation for pure Yang-Mills Lagrangian

Toffomat's answer is a great answer. Let me try to add a little bit more physical motivation for what it means to "decouple the ghosts." SUMMARY: The requirement of gauge invariance comes ...
Luke Pritchett's user avatar
1 vote

Motivation for pure Yang-Mills Lagrangian

Classical Yang Mills theory is a generalisation of classical EM. More precisely, it generalises the gauge structure group from an abelian group like $U(1)$ to non-abelian group like $SU(2)$ or $SU(3)$....
Mozibur Ullah's user avatar
1 vote

Can Black Holes with electroweak or strong interactions exists in General Relativity or in Supergravity?

You can definetely add to GR other interactions different from EM. You just need to be careful on what the meaning (physically intended) of such model is. For example, QCD is used in order to model ...
LolloBoldo's user avatar
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1 vote

Commutation in the Local Gauge Transformations

The Wiki link given by @Prahar is useful, but it does not seem to include the integral form $$ e^{-X} e^{X+\delta X}= 1+\int_0^1 e^{-tX} \delta X e^{tX} dt+ O[(\delta X)^2], $$ that I think easier to ...
mike stone's user avatar
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1 vote

Dirac field coupling to gauge fields

The difference between the Lagrangian densities (1) and (2) is a total derivative term, which doesn't change the EL equations. See also e.g. this related Phys.SE post.
Qmechanic's user avatar
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1 vote

Is color charge internal symmetry or global symmetry?

I would prefer to say that $SU(3)$ is an internal gauge symmetry, and color charge is not physically observable because it is not gauge invariant. The permutations of colors you mentioned is one ...
11zaq's user avatar
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1 vote
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Mathematical description of higher spin gauge theories

The answer depends on what kind of consistent higher spin theories you are interested in. There are several examples: in $3d$ simple higher spin gravities are just Chern-Simons matter theories (note ...
John's user avatar
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