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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282 views

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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134 views

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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284 views

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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813 views

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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382 views

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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160 views

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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70 views

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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161 views

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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126 views

Variational derivatives of strongly connected diagrams functional in gauge theory

Background In Jorge C. Romao's "Advanced Quantum Field Theory", at the end of page 218, Eq (6.266) reads: $$\tag{1} \left.\frac{\delta^{2}}{\delta \omega^{b}(y)\delta A_{\mu}^{c}(z)}\left[ \frac{\...
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143 views

Transformation Law for Covariant Derivative in $SU(2)$ Yang-Mills

In page 488 of Peskin and Schroeder, it is stated (emphasis mine): It is not difficult to check using (15.27) and (15.21) that, even for finite transformations, the covariant derivative has the ...
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392 views

Does spontanous symmetry breaking affect Noethers theorem?

Does spontanous symmetry breaking affect the existence of a conserved charge? And how does depend on whether we look at a classical or a quantum field theory (e.g. the weak interacting theory)? (...
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604 views

Gauge invariance and Feynman path-integrals

Let me look at the Hamiltonian of a charged particle in a plane in a constant magnetic field ($\vec{B}$) pointing upwards - then in usual notation it is, $$\hat{H} = \frac{1}{2m}\biggl(\hat{p} + \...
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2answers
58 views

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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1answer
183 views

Georgi-Glashow model and the VEV of the scalar field

Consider the Georgi-Glashow model, an $SU(2)$ gauge theory with a real scalar in the adjoint (thus a 3-vector in the colour space) $\phi$. The Lagrangian is $$ L = -\frac{1}{4g^2} F_{\mu \nu}^{\, a} ...
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210 views

Charged CFT observables and AdS/CFT

I have a simple question regarding the holographic dictionary when mapping operators on the CFT side to those in AdS. One piece of the dictionary is that a global symmetry maps onto a gauge symmetry ...
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1answer
208 views

Why is the Yang-Mills Comparator unitary?

In chapter 15.2 of Peskin, the comparator is defined, as some object $U\left(y,\,x\right)$ which transforms as: $$ U\left(y,\,x\right) \mapsto V\left(y\right) U\left(y,\,x\right) \left[V\left(x\right)^...
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191 views

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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79 views

Is there an algorithm to diagonalize a matrix using gauge transformations

I have two matrices $U(\lambda, x,t)$ and $V(\lambda, x,t)$, where $\lambda$ is a parameter, which belong to the $sl(2)$ algebra, and satisfy the zero-curvature equation $$ \partial_t U - \partial_x V ...
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183 views

BRST quantization and norm

States with definite ghost number have zero norm (since ghost number is anti-hermitian and has real eigenvalues). E.G. when quantizing relativistic point particle, physical spectrum turns out to ...
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53 views

What is the status of gauged gravity [duplicate]

The Standard Model of elementary particles is a gauge theory with gauge group $SU(3)\times SU(2)\times U(1)$, which is really a successful theory. We might be able to quantize gravity similarly. ...
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114 views

Can you gauge a $U(1)_L$ symmetry?

I recently calculating the one loop correction for the propagator of a gauge boson, $\hspace{5cm}$ I assumed arbitrary left and right couplings, $ g _L $ and $ g _R $. I found that the one loop ...
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256 views

The 6-j symbol and intersecting Wilson loops, redux

This is a quite specific question continuing the problems I have with computing the expectation value of intersecting Wilson loops I laid out here. Using the tools from the answer there, I quite ...
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93 views

Why does strong interaction increase with distance?

I read numerous times that strong interaction increases with distance. But how can one actually derive the force-distance relation from the lagrangian (quark field + gluon field + gauge coupling)? ...
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152 views

(coordinates) Invariance/Covariance of Chern-Simons theory and Yang-Mills theory

It is known that 3D Chern-Simons(C-S) theory has no explicit metric involving in the Lagrangian density: $$ A \wedge dA + (2/3) A \wedge A \wedge A $$ while the 4D Yang-Mills(Y-M) theory has the ...
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146 views

Noether current for the Lagrangian without Lorentz invariance

I am reading an article by Watanabe & Murayama. It gives a proof on the counting of Nambu–Goldstone bosons without Lorentz invariance. I am trying to derive all the equations to get a better ...
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184 views

What is the fundamental difference between ghost and auxiliary fields?

I am somehow confused by the notion of auxiliary fields, such as for example the fields $F$ and $D$ which appear in supersymmetry, and the notion of ghost fields which appear for example in the BRST ...
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164 views

Master Field Large N limit

I would like to ask a question about the so-called ''Master Field''. As far as I understand, this represents a classical configuration in the large n limit (saddle point solution) but there is no ...
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89 views

How do you simulate a quantum gauge theory in a gauge with negative norms on a quantum computer?

How do you simulate a quantum gauge theory in a gauge with negative norms on a quantum computer? There are some gauges with negative norms. It's true that if restricted to gauge invariant states, the ...
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106 views

Gauge invariance in classical electrodynamics

I think that I don't fully understand concept of gauge invariance. Suppose we have a Lagrangian for classical ED which is: $$\mathcal{L} = -\frac{1}{4} (F_{\mu \nu})^2 - j^{\mu}A_{\mu}.$$ First part ...
4
votes
1answer
180 views

Is there a method which quantizes non-abelian gauge theories without path integrals formalism?

In the most QFT books there is a method of quantization of non-abelian theories through path integral methods. But I want to learn also the other methods without using of this formalism. Does anyone ...
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3answers
785 views

Multivariable Dirac Delta and Faddeev-Popov Determinant

From this mathstack page and in particular Qmechanic's answer: There exists an $n$-dimensional generalization $$\tag{1} \delta^n({\bf f}({\bf x})) ~=~\sum_{{\bf x}_{(0)}}^{{\bf f}({\bf x}_{(0)})...
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468 views

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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155 views

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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1answer
183 views

$SU(2)$ gauge symmetry

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{...
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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 ...
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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 ...
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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 ...
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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 ...
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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}_{\,\,...
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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 ...
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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 ...
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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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1answer
603 views

Classical theories and AdS/CFT

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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1answer
331 views

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 \begin{equation} A = \omega(r)\...
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512 views

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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1answer
91 views

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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282 views

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 ...
4
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1answer
155 views

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 ...
4
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1answer
420 views

The BRST construction for YM with or without auxiliary field

I'm learning BRST symmetry for Yang-Mills theory and I see that there are two ways of writing BRST differential. In some books (for example Ryder's and Ramond's textbooks) BRST differential acts as \...
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252 views

What is the constraint on the Gauge Potential in the Covariant Gauges?

One of the most common gauges in QED computations are the $R_{\xi}$ gauges obtained by adding a term \begin{equation} -\frac{(\partial_\mu A^{\mu})^2}{2\xi} \end{equation} to the Lagrangian. ...