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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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Particles and associated fields

When a particle is associated with a field. 1) It is said that the excitation of the field produces the particle, 2) it is also said that when the field is quantized, the quanta of the field is ...
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Reference request for Gribov ambiguity

I was hoping to find a reference (book or article) with a good introduction to the Gribov Ambiguity in non-abelian gauge theories. I’ve looked through QFT books by Schwartz and Srednicki, Rubakov’s ...
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Gribov's phenomenon

In the well known textbook by Itzykson-Zuber "Quantum Field Theory" there is a discussion of the Gribov phenomenon in non-abelian gauge theories (see Section 12-2-1). To my taste, the discussion ...
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Polar representation of complex scalar field in spontaneous symmetry breaking

In Rubakov's "Classical Theory of Gauge Fields", in the chapter on Higgs mechanism, he mentions that you can switch to the polar form of the complex scalar field only for non-zero vacuum value of the ...
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Gauge invariance on Yang-Mills Lagrangian

How do I verify the invariance on Yang-Mills' Lagrangian: $$L = -\frac{1}{4} \sum_{a} \left(\partial_\mu A_\nu^a - \partial_\nu A_\mu^a + gf^{abc}A_\mu^bA_\nu^c \right)^2$$ under the transformation:...
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Simplify Yang-Mills Equation of Motion in the 1-form gauge field $A$

We know the Yang-Mills theory Equation of Motion (eom) without source $$ * D * F = * (d (* F ) + [A, (* F )])= 0. $$ My question is that what are the most simple form we can boil down this ...
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Classical Yang-Mills equation of motion with both electric and magnetic sources?

We know the classical Maxwell equation of motion (eom) with both electric and magnetic source can be written as: (1) Explicit form or more schematically as: (2) Differential form $$ d * F = * J_e $$...
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$U(N)$ & $SU(N)$ : What's the conceptual difference in Gauge Theory?

I know the mathematical difference that one means $ absolutevalue(det) = 1$ and one means det = 1 (rotation) and that ones the subgroup of the other and so on. But: has a local/gauged $SU(3)$ ...
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Mistake or Rewriting of Yang-Mills in Nakahara

I am familiar with Yang-Mills equation of motion E.O.M. (without matter or source fields) in differential form. $$ D * F =0 $$ and Bianchi identity $$ D F=0 $$ where $F= dA + A \wedge A$ and $D=d + [...
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Connection between gauge invariance and Lorentz invariance

This question is presented in the context of Weinberg's QFT book treatment, in particular considering the electromagnetism chapter. It begins in chapter 5 where Weinberg argues that in order to have ...
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Interpreting the conserved charge in scalar QED

In scalar QED, applying Noether's theorem for internal global symmetries results in a Noether current that is dependent on the gauge because of the presence of the covariant derivative. $$j_\mu=-i(\...
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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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Why does a triangle anomaly appear in a gauge theory?

I have read that when we construct a theory with abelian gauge symmetry there will appear some anomalies when we do the quantum correction to the theory. In 4D space such anomalies are explained by ...
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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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What is $U(1)$ symmetry?

I saw there are three intrinsic symmetries in physics,U(1),SU(2) and SU(3).What's the U(1) symmetry talking about?I would appreciate it if you can give me some explaination.
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Is it always possible to move to the “Cartan Gauge”?

Forgive me for potentially coming up with a new name for what I am about to describe. Let's say we have a scalar field $\phi^a$ which transforms with respect to the adjoint representation of some Lie ...
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Gauge group of Electroweak theory

I am doing a question that asks me to identify the gauge groups of a Lagrangian with the field strength tensors $$\bf{F}_{\mu \nu} = \partial_{\mu}\bf{W}_{\nu} - \partial_{\nu} \bf{W}_{\mu} - g\bf{...
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If the gauge symmetry is not broken by spontaneous symmetry breaking, what symmetry is broken?

In this post, the answer by buzhidao showed that the $U(1)$ gauge symmetry is not broken by spontanous symmetry broken and Higgs mechanism. What role does "spontaneously symmetry breaking" ...
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A Question about Wess-Zumino Gauge in Non-Abelian Gauge Theory

I have a question about the Wess-Zumino gauge in non-Abelian supersymmetric gauge theory. I am following BUSSTEPP Lectures on Supersymmetry. The spinortial field strength is defined as $$W_{\alpha}(...
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Z and $\gamma$ bosons as mixtures of W and B: Part II

When it is said that the photon is ["a mixture of W and B"][1] ($B$ being a gauge field associated with the $U(1)$ hypercharge) I have one question on this: Why there isn't a boson directly ...
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Gauge fixing in canonical quantum gravity

In analogy with QFT, the partition function in canonical quantum gravity is defined as a functional integral over the metric tensor (which is now the quantum field), $$ \int \mathcal{D} g \mathcal{D}\...
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Z and $\gamma$ bosons as mixtures of W and B: Part I

When it is said that the photon is "a mixture of W and B" ($B$ being a gauge field associated with the $U(1)$ hypercharge) I have a question on this: When speaking of "mixtures", this is meant as ...
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Motivation for Weinberg angle in electroweak gauge interaction?

Suppose I have the following lagrangian If we only focus on the neutral current in the lagrangian: Where $L$ is defined as: And $Y_L$,$Y_{R}^{\nu}$,$Y_{R}^{e}$, are the hypercharge values of the ...
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Why do we require gauge symmetries to commute?

My question arises after reading the 87th page of Elementary particle physics in a nutshell by Tully: which is also given by the following link: https://books.google.se/books?id=vLy2YlkXZuEC&pg=...
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Why does the divergence of a QFT's coupling constant under RG flow trivialize the theory if it occurs in the UV but not in the IR?

When you first learn quantum field theory, at some point you calculate the beta function (to leading order) for a renormalizable coupling constant of some theory like $\varphi^4$ theory, Yukawa theory,...
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How do I show that the Lorenz gauge is consistent?

I have been asked to show that the Lorenz gauge condition, written as $$\nabla_T \bullet \vec{A} + \dfrac{1}{c^2}\dfrac{\partial}{\partial t}\Phi = 0$$ is mathematically consistent with the vector ...
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Noether current and continuity equation in classical scalar QED

Consider the following scalar QED model \begin{align} S = \int \mathrm{d}^{d+1} x\, \left\{-\left(\mathrm{D}_{\mu}\phi\right)^{\dagger} \left(\mathrm{D}^{\mu}\phi\right) -m^2 \phi^{\dagger}\phi - \...
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Symplectic group $Sp(2N)$ in Srednicki's book

There is a question in Mark Srednicki's Book (Problem 24.4, p.160) about $Sp(2N)$, but I am not sure I understand the significance (application?) of this group. In that chapter, he talks about $SO(N)$ ...
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Gauge theory in Condensed Matter physics

Always come across these two jargons, namely Matter Field and Gauge Field, please explain what is the difference between them and why it is important in condensed matter physics? There are many ...
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Non-Abelian Gauge Field and Fermions Under Parity?

Under a discrete parity transformation, how does a non-abelian gauge field $A^a_{\mu}(x)$ transform? Is it possible to get mixing between the colors? How about the fermion $\psi_n(x)$ which is coupled ...
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Could electroweak interactions derive from higgsing of gauged chiral symmetry?

A recent question discussed the practice of introducing electroweak interactions into chiral perturbation theory by gauging part of the chiral symmetry. Gauging chiral symmetry is normally regarded as ...
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Silly Question about Supersymmetric Gauge Theory

In $\mathcal{N}=1$ super electrodynamics, one has the following vector superfield $$V(x,\theta,\bar{\theta})=\bar{\theta}\bar{\sigma}^{\mu}\theta v_{\mu}(x)+\bar{\theta}^{2}\theta\lambda+\theta^{2}\...
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Covariant derivative of a composite field and the chain rule

I have a gauge theory with some rather strange covariant derivatives and I am wondering how they act on a composite field like $\psi= \phi\psi'$. In my setup, the covariant derivative acting on a ...
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Showing the form of the covariant derivative of $\phi$, if $\phi$ transforms as the adjoint representation of $SU(n)$

I want to show that if $\phi$ transforms as the adjoint representation of SU(n), its covariant derivative is given by $\textbf{D}_\mu \phi = \partial_\mu \phi + i [\textbf{A}_\mu, \phi]$. (Exercise in ...
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Reference on instantons in gauge theories

Is there a reasonably detailed and systematic exposition of the theory of instantons in non-abelian gauge theories?
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A Question About Vector Superfield

My reference is section 5.2 of BUSSTEPP Lectures on Supersymmetry, page 46. A Vector superfield $V$ is a scalar superfield which satisfies the reality condition $$V=\overline{V},$$ where the bar ...
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Can the Dirac quantization condition be derived within Lev Vaidman's formalism without gauge fields?

Textbooks often claim that phenomena like the Aharonov-Bohm effect require that any local formulation of quantum gauge theory use gauge potential fields. (It's also sometimes claimed that the A-B ...
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Gauge and global symmetries in Chern-Simons/WZW correspondence

I am trying to understand how bulk gauge symmetry in 3d Chern-Simons theory becomes a global symmetry in the boundary 2d WZW theory. In particular, I am trying to understand the papers by Elitzur et ...
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Gauge dependence of the Einstein tensor and the Riemann/Ricci curvature tensors in non-linear general relativity

The Einstein field equations are given by (with assuming $\Lambda = 0$), $$ R_{ab} - \frac{1}{2} R g_{ab} = \kappa T_{ab}. $$ The principle of general covariance states that the form of these ...
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Compactification of space in Hamiltonian formulation of Yang-Mills theory

I am reading David Tong's lecture notes on Gauge Theory where he talks about Hilbert space interpretation of Yang-Mills theories in Section 2.2 of Chapter 2. When discussing the gauge dependence of ...
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Conservation of magnetic charge

It is well known that the electric charge of a system can be thought of as the Noether charge associated with isotropic large gauge transformations. That is, given Einstein-Maxwell theory $$S=\frac{1}...
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Gauge fixing in Ginzburg-Landau simulation

I am developing a computer simulation of the Ginzburg-Landau model of superconductivity. In a few words, I have discretized the domain with finite differences and I am using Nonlinear Conjugate ...
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1answer
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Covariant derivative in field theory

I'm reading Physics from Symmetry by Jakob Schwichtenberg and in Chapter 7 he introduces the covariant derivative when deriving the interaction Lagrangian density for the spin-half - spin-1 field: $$ ...
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Fields transforming under an exceptional Lie group

We may think of tensors as sections of an associated vector bundle to a principal $\mathrm{GL}(n,\mathbb R)$ bundle, with a fibre chosen to be $\mathbb R^m \times (\mathbb R^*)^n$ - these play a role ...
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Unitary gauge for spontaneous symmetry breaking

I'm given a lagrangian $$ \mathcal{L} = \partial_{\mu} \Phi^{\dagger} \partial^{\mu} \Phi + m^2 \Phi^{\dagger} \Phi - \lambda (\Phi^{\dagger} \Phi)^2 $$ where $m^2 > 0, \lambda > 0$. This ...
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Can we choose polarization vectors freely in any given gauge theory?

When quantizing a gauge theory, we obtain spin-1 particles propagating in space-time. When we want to count the degrees of freedom of the theory or, equivalently, when we are trying to decompose the ...
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Is the supercurrent gauge invariant?

If we consider ${\cal N}=1$ renormalizeable chiral gauge theories, specifically discussed in section 27.4 of Weinberg's Quantum Theory of Fields, Supersymmetry book, should the supercurrent be gauge ...
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A Naive Question about Gauge Theory

I am suffering from a question I encountered from the lecture notes of gauge theory by David Tong. The problem comes from page 67 on the gauge fixing in back-ground gauge method. In David Tong's ...
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What classifies gaugings?

Gauging a global symmetry $G$ introduces several free parameters to the theory. For example, In $d=4$, gauging a simple and simply-connected Lie group introduces a coupling constant and a theta term, ...
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How can I compute the spin texture for a $SU(2)$ gauge model?

I am trying to determine the helicity of 4 Dirac cones in my model, and one way I want to approach it is by plotting the spin-texture. However, I am unsure of how one would calculate the spin-texture ...