# Tagged Questions

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. ...

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### About the gauge formalism in statistical quantum field theory

I would like to understand a bit more the aspects of the gauge theory in statistical field theory. In particular, I would like to understand how the replacement $\tau \rightarrow it/\hbar$ is ...
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### 4D instantons and the moduli space of N=2 on R^3 x S^1

I am reading the paper arXiv:0807.4723 by Gaiotto, Moore, and Neitzke on wall-crossing. I would like to understand whether if the Darboux coordinates in the mutually non-local case contain the ...
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### Aharonov-Bohm Effect in Torus

I had a very brief introduction to the Aharonov-Bohm effect in class. The lecturer introduced the notion that $H(\Phi=\Phi_0)$ and $H(\Phi=0)$ gives identical energy spectrum and that the Hamiltonians ...
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### Gauss law in classical U(1) gauge theory

I can see that $a_{0}$ is not an independent field and Gauss law is a constraint on the theory arising from field equations. But, I don't get the geometrical picture. Let $A$ be the space of all ...
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### Taking the continuum limit of $U(N)$ gauge theories

I would like to draw your attention to appendix $C$ on page 38 of this paper. The equation $C.2$ there seems to be evaluating the sum $\sum_R \chi _R (U^m)$ in equation 3.16 of this paper. I ...
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### Is the distinction between the Poincaré group and other internal symmetry groups artificial?

For instance, given a theory and a formulation thereof in terms of a principal bundle with a Lie group $G$ as its fiber and spacetime as its base manifold, would a principle bundle with the Poincaré ...
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### Particle on $S^1$ and $U(1)$-principal bundle

I have a question arisen from a simple QM problem: let consider a boson on $S^1$ minimally coupled with a constant gauge field $A$. Taking the stationary Schrödinger (S) or Klein-Gordon (KG) equation ...
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### When do gauge theories have protected gapless excitations?

Goldstone's theorem states that a system in which a continuous symmetry is spontaneously broken necessarily has gapless excitations. (A hand-waving "proof" of Goldstone's theorem can be given by ...
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### Why cannot a fundamental string couple to the R-R gauge field $C_{\mu\nu}$?

People usually say that D-branes can carry R-R charges, or can couple to R-R sector gauge fields. But why a fundamental string cannot couple to a 2-form R-R sector gauge field? What's the essential ...
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### How do people historically have come to use the Yang-Mills theory in physics?

There are many books, in which Yang-Mills theory is introduced "just like that". But I didn't find some book with set of historical arguments, which had led people to using it in quantum field theory. ...
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### How many physical degrees of freedom does the $\mathrm{SU(N)}$ Yang-Mills theory have?

The $\mathrm{U(1)}$ QED case has two physical degrees of freedom, which is easy to understand because the free electromagnetic field must be transverse to the direction of propagation. But what are ...
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### What is the relationship between BRST symmetry and gauge symmetry?

As far as i know the BRST symmetry is an infinitesimal (and expanded) version of gauge symmetry. Recently I read the following: "when QFT was reformulated in fiber bundle language for application to ...
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Take the Lagrangian with one fermion: $$\mathcal{L} = -\frac{1}{4}F^{\mu\nu}_aF^a_{\mu\nu} + \bar{\psi}(i\gamma^\mu D_\mu - m)\psi$$ where the gauge covariant derivative $D_\mu = \partial_\mu+i\frac{... 1answer 122 views ###$U(1){\times}U(1)$local gauge invariance derivative In QED and the basic Higgs mechanism, there is a local gauge transformation where a scalar field$\phi$is transformed as:$e^{i\theta\eta(x)} \phi$The partial derivative of this however makes the ... 1answer 327 views ### Moose Models (Purpose, Examples) A problem set for my QFT class is titled "Moose Models" and deals with the moose model for a gauge symmetry of$U(1)\times U(1)$. I was wondering if I could get an explanation of what a Moose Model ... 1answer 706 views ### QED BRST Symmetry This is a homework problem that I am confused about because I thought I knew how to solve the problem, but I'm not getting the result I should. I'll simply write the problem verbatim: "Consider QED ... 2answers 986 views ### Counting degrees of freedom in presence of constraints In a$N$dimensional phase space if I have$M$1st class and$S$2nd class constraints, then I have$N-2M-S$degrees of freedom in phase space. How can I calculate the degrees of freedom in ... 1answer 436 views ###$SU(2)$Yang-Mills EOM I'm having trouble with some indices on my yang-mills lagrangian. I have a gauge group$SU(2)$and a field strength tensor$$F_{ab}^{i}=\partial_{a}A^{i}_{b}-\partial_{b}A^{i}_{a}+\epsilon^{i}_{\,\,... 2answers 98 views ### Anomalous Slavnov-Taylor identity I will be happy if someone could clarify the mystery here. Consider the following derivation of the anomalous Slavnov-Identity. It's based on lecture notes by Adel Bilal. Suppose we have an action ... 1answer 85 views ### What gauge field can be constructed from Lorentz symmetry? You can take a global symmetry and promote it to a local gauge symmetry by introducing an appropriate gauge field and upgrading the partial derivative to a covariant derivative. The photon field ... 1answer 289 views ### A naive question on the Quantum Hall Effect(QHE) and the confinement in gauge theory? The non-interacting 2D lattice QH system is described by the Hamiltonian$H=\sum t_{ij}e^{iA_{ij}}c_i^\dagger c_j+H.c$My confusion is: Does this imply that the$2D$lattice QHE is described by the$...
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When I was editing the Physics.SE tag wiki for ads-cft, I initially wrote something on the lines of : The AdS/CFT correspondence is a special case of the holographic principle. It states that ...
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### Einstein-Yang-Mills Connections

I am playing around with coupling a classical $SU(2)$ Yang-Mills theory to Einstein's equations. Assuming spherical symmetry, the $SU(2)$ connection can be written A = \omega(r)\...
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### Non-inertial frames in Lagrangian mechanics?

Building on this Phys.SE post I am interested in how non-inertial frames can be considered in Lagrangian mechanics. My understanding is that changing the reference frame causes a transformation of the ...
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### Why is $U(1)$ special when defining global charges?

For gauge groups like $SU(2)$ and $SU(3)$ etc. we know that observable states such as mesons or baryons must be charge neutral. However, for a $U(1)$ gauge group we can have charged initial states in ...
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### Wess-Zumino Gauge in non-Abelian supersymmetric theory

I've got a question concerning non-Abelian supersymmetric gauge theories. Consider supersymmetric non-Abelian theory realized on chiral superfields $\Phi_i$ in a representation $R$ with matrix ...
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### How to see the ground state degeneracy (GSD) from a $BF$ theory in $2+1$ $d$?

I have seen many times the $BF$ theory has non-trivial ground state degeneracy (typically on torus), but I can not see how the conclusion come out. Recently I found a paper by Hansson, Oganesyan and ...
One of the most common gauges in QED computations are the $R_{\xi}$ gauges obtained by adding a term $$-\frac{(\partial_\mu A^{\mu})^2}{2\xi}$$ to the Lagrangian. ...