# Questions tagged [gauge-theory]

A gauge theory has internal degrees of freedom that do not affect the foretold physical outcomes of the theory. The theory has a Lie group of *continuous symmetries* of these internal degrees of freedom, *i.e.* the predicted physics under any transformation in this group on the degrees of freedom. Examples include the $U(1)$-symmetric quantum electrodynamics and other Yang-Mills theories wherein non-Abelian groups replace the $U(1)$ gauge group of QED.

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### Gravity from algebra

Can someone provide me a reference that describes the gauging of the Poincare algebra to obtain Einstein's relativity? "It is well known that Einstein’s formulation of gravity can be obtained by ...
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### GR as a gauge theory: there's a Lorentz-valued spin connection, but what about a translation-valued connection?

Given an internal symmetry group, we gauge it by promoting the exterior derivative to its covariant version: $$D = d+A,$$ where $A=A^a T_a$ is a Lie algebra valued one-form known as the connection ...
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### Commutators in Gupta-Bleuler formalism for quantization of the electromagnetic field

In the Gupta-Bleuler formalism we have for the canonical momenta $$\pi_\mu=F_{\mu0}-g_{\mu0}\partial_\alpha A^\alpha.$$ Every resource I find online say that the equal time canonical commutation ...
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### Counting degrees of freedom in the Higgs mechanism for different gauges

I am wondering how to count the degrees of freedom (dof) for a massive gauge field in different gauges. I've been reading some other answers, but haven't found a solution yet. I am looking at the ...
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### Infinitely many conserved currents in any QFT?

So I have the following curiosity: Consider for example, in QED, the quantity $$j^\mu\equiv\partial_\nu (\lambda(x) F^{\mu \nu})$$ where $\lambda(x)$ is an arbitrary scalar function of spacetime, ...
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### Local charge current for gauge field and conservation of charge

Motivation: It is a well known fact that the gravitational field (in General Relativity and direct generalizations of it) has no local energy-momentum density. Usually there are two reasons stated, ...
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### Are internal string states analogues of internal particle states?

It is sometimes said that in string theory elementary particles correspond to modes of vibration of a string. Likewise in QFT, several particle fields take their values in a higher dimensional space,...
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### $USp$ global symmetry in $d=3$, ${\cal N}=4$ supersymmetric QFT

Define a 3-dimensional QFT with $N=4$ supersymmetry (4 supercharges), and the field content is $g$ $N=4$ hyper-multiplets (that are in a representation $R$ of some group $G$). Each hyper-multiplet is ...
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### Showing that $U(1)_R$ charge is non-anomalous in SUSY QCD when $r=\frac{F-N}{F}$

I'm trying to show that the value of the R-charge $r$ for which the R-symmetry is non-anomalous is given by $r=\frac{F-N}{F}$. To do this we must calculate the triangle diagrams for the quarks \$\...
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### What is the effect of including additional representations in the action of a lattice gauge theory?

I'm reading Introduction to Quantum Fields on a Lattice by Jan Smit. When introducing the lattice gauge-field action as a sum over plaquettes, Smit says that in general the action should include a sum ...
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### Vector Potential of a rotating Spherical Shell

I have done all the calculation in finding the vector potential leading up to the equation 5.68. But then Prof. Griffiths goes back to the original figure and mentions that the coordinate of the point ...
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### Which of the Wightman axioms are not incorporated by four dimensional quantum Yang-Mills?

I am trying to understand the quantum Yang-Mills existence problem but the best I have seen so far is the statement that there is no known interacting relativist field theory in four dimensions which ...