# 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.

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### How does the underlying symmetry of QCD imply the allowance of a 4-gluon vertex?

Quantum chromodynamics allows for a four-gluon vertex such as this, in a diagram Such a vertex would never be allowed in quantum electrodynamics, which has an underlying U(1) gauge symmetry. I know ...
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### Time reversal symmetry of the Faddeev-Popov determinant

I am studying the Faddeev-Popov procedure to quantize a non-Abelian gauge theory, and I got confused by the status of the time reversal symmetry. People have different definitions of the time reversal ...
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### Yang-Mills Bianchi identity in tensor notation vs form notation

I've seen the Yang-Mills Bianchi identity written as both $$0 = dF^a + f^{abc} A^b \wedge F^c$$ and, in tensor notation, as $$\epsilon^{\mu\nu\lambda\sigma}D_{\nu} F^a_{\lambda\sigma} = 0.$$ Here ...
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### Fierz identity for symplectic group

For the fundamental representation of $SU(N)$, there is a Fierz identity: $$\sum_iT^i_{ab}T^i_{cd}=\frac{1}{2}\left(\delta_{ad}\delta_{bc}-\frac{1}{N}\delta_{ab}\delta_{cd}\right)$$ where $T^i$ is ...
1answer
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### 2-dimensional QFTs invariant under area-preserving diffeomorphisms

In introductory textbooks & lecture notes on conformal field theory, it is usually stated that solving the highly nontrivial dimensional quantum field theory in 2 dimensions is possible due to the ...
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### Yang-Mills Action for Non-Trivial Bundle

Suppose we have a principal $G$ bundle $(P,M,π)$ where $M$ is a 4-dimenational manifold and $G$ a Lie group (and $\mathfrak{g}$ its Lie algebra).The Yang Mills action is a functional of the gauge ...
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### $CP$ Invariance of Yang-Mills Vacua in Electroweak Theory

It is well know that quantum Yang-Mills theory has a periodic vacuum structure. Consider electroweak theory. For a single generation of fermions, the theory is CP invariant. I would like to know if ...
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### Why Is Abelian Gauge Theory So Special?

I have a perhaps stupid question about Maxwell equations. Let $G$ be a generic Lie group. We consider a $G$-gauge theory. Let $A$ be the associated connection $1$-form, and $F=dA+A\wedge A$ be the ...
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### Questions about BRST symmetry [closed]

For a course about the standard model, I am writing a paper on BRST symmetry. For this I am mainly following the material developed in chapter 16.4 of Peskin and Schroeder. I am mostly done, however ...
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### Why aren't gravitons spin 1?

Expressing the metric as $g_{\mu \nu} = \eta_{\mu \nu} + h_{\mu \nu}$, assuming $h_{mu \nu} \ll 1$ we can write the Einstein Hilbert action to leading order in $h_{\mu \nu}$ and quantize the ...
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### Relating the Yang-Mills field-strength to the Maxwell tensor in $SU(2)$ gauge theory

I'm studying topological monopoles in a $SU(2)$ Yang-Mills theory with spontaneous symmetry breaking, through the book "Topological Solitons", by Manton and Sutcliffe. In section 8.2, the authors ...
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