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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Form of the optical theorem in non-Abelian theory

I am studying chapter 16.3 from Peskin & Schroeder and I am trying to follow through the argument where we include contributions from ghosts to satisfy the Ward identity in non-Abelian gauge ...
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Nonlinear symmetry realization: what is it for and caveats

I have several doubts regarding the nonlinear realization of a spontaneously broken symmetry and hope they are approppriate to be grouped, and I appreciate any insights. Consider the group breaking ...
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Showing that the integration measure is preserved under gauge transformation in the non-Abelian case

I am trying to show that the integration measure we use in the Fadeev-Popov method of quantisation of non-Abelian gauge theory is invariant under a gauge transformation. I am using Peskin & ...
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From where can I study $SU(2)\times U(1)$ Symmetry Breaking [duplicate]

I have done till $U(1)$ Symmetry Breaking for my master's thesis and need to do $SU(2)\times U(1)$ Symmetry Breaking. My supervisor suggested the book 'Gauge theory of elementary particle physics' for ...
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Steps in Quantizing Electromagnetic Field for the Gauge Condition $A_0=0$

While reading section 9.3 of QFT An Integrated Approach by Fradkin, it is shown (see equations $(9.49)$ and $(9.54)$ of the book) $$B_{j}(\boldsymbol{x})^{2}=\boldsymbol{p}^{2} A_{j}^{T}(\boldsymbol{p}...
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Does Yang-Mills have free gauge bosons?

Is there any physical problem with a propagating non-Abelian gauge boson? That is, a plane wave mode $A_\alpha^\mu e^{ikx}$, where $A_\alpha^\mu=b_\alpha\epsilon^\mu$, with $b_\alpha$ a constant ...
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Solution to Dirac equation with external source

The Dirac equation is: \begin{equation} \left[i\gamma^{\mu}(\partial_{\mu}-iA_{\mu})-m\right]\psi=0, \tag{1} \end{equation} where $A_\mu$ is a gauge field. The solution to this equation is:...
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Antifields in BV formalism - do they also have gauge transformation laws?

I am studying Weinberg Vol 2 and the BV formalism of the gauge theory. There, the antifields are introduced somewhat out of thin air. I am a little bit confused about their properties. For example, ...
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How is the interaction of leptons and quarks with gauge fields organized in the Standard Model?

Well, standard model has $SU(3)\times SU(2)\times U(1)$ gauge group, so this is a direct product of multiple groups embedded in larger set. So how quarks that must interact with every gauge field and ...
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Wilson loops as representations of the Lorentz group

Wilson loops in lattice $4d$ Yang-Mills theory are used to build various glueball states of different spins when they are applied to the vacuum. The spin dependence of such states is related with the ...
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Sources to learn Gauge Theory, Groups, Lie Algebra, etc [duplicate]

As seen in previous questions, I'm interested in gauge theory, although I have no idea how to do any of the mathematics, though i'd like to start. With that in mind, Are there any good sources that ...
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What does it exactly mean by right and left functional derivatives?

In BV formalism of the gauge theory, we need to compute the right / left functional derivatives of the actions that include fermions. I do not quite see what it means by that. For example, let us ...
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Chern-Simons Realization of Dijkgraaf-Witten Theory

There is a realization of $Z_N$ Chern-Simons theory (Dijkgraaf-Witten theory) using an instance of $U(1) \times U(1)$ Chern-Simons theory. As explained on page 38 of https://arxiv.org/abs/2007.05915 , ...
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What are the numerical values of the gauge coupling constants? [duplicate]

I mean the values of: $U(1)$ gauge coupling $SU(2)$ gauge coupling $SU(3)$ gauge coupling
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Non-Abelian vertex 3-gauge-boson

I am trying to understand how the vertices depicted in page 507 of Peskin and Schroeder come about. I understand that vertex where we have 1 gauge boson and two fermions but I'm confused on the ...
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Is my expression of the Noether current $J^\mu$ for a local $\rm U(1)$ symmetry correct? If not, what's wrong?

The Lagrangian of electrodynamics reads $$\mathcal{L}=i\bar\psi\gamma^\mu D_\mu\psi-m\bar\psi\psi-\frac{1}{4}F_{\mu\nu}F^{\mu\nu}$$ where $D_\mu=\partial_\mu+iqA_\mu$. It is unchanged under the set of ...
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Yet more gauge group nonsense: $D3$? $Q8$? $Z8$?

This'll probably make me look like a total idgit, but I have a new question in the same vein as mine about $SU(4)$, but this time without any guesses. I've looked a bit into groups, and it looks like ...
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What would the force arising from an $SU(4)$ gauge field operate like? (As in, how many charges, whether the boson would interact with the force, etc)

Heyo, i'm new to this all, and deadly curious what this would look like. If this isn't specific enough, lemme know.
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Vanishing of path integral over internal d.o.f. of test particle in $SU(N)$ gauge theory

In Ch-2 (Yang-Mills theory) of David Tong’s notes on gauge theory. Tong writes an action $$S_w=\int d\tau \hspace{2pt}i w^{\dagger} \frac{dw}{d\tau}+\lambda(w^{\dagger}w-k)+w^{\dagger}A(x^{\mu})w\tag{...
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Abelian Gauge Theory

Hello everyone I have a question on this exercise from my Supersymmetry class in 4d ${\cal N}=1$. Given a $\text{U}(1)^3$ gauge theory with 9 chirals $A_i , B_j , C_k$ with $i,j,k$ running from 1 to 3 ...
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Advantages of using the potentials $A$ and $\phi$ instead of the fields $E$ and $B$ [duplicate]

I'm taking a quantum mechanics course and we briefly reviewed some facts of ED, namely the Maxwell equations and their equivalent version by expressing the electric field $E$ and magnetic field $B$ ...
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Can we say tension is the ability to generate interference by this paper?

https://arxiv.org/abs/1206.2021 Abstract : We propose a method for measuring the string tension in gauge theories, by considering an interference effect of mesons, which is governed by a space-time ...
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Area and perimeter

Apparently (?), a line operator over a very large loop with length $L$ can obey either perimeter law or area law, $-\log\langle U\rangle\sim L^a$ with $a=1,2$, respectively. We call these options &...
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What is a propagating degree of freedom?

Given a gauge field theory, the various fields involved have (pointwise) degrees of freedom. For instance, if I consider the gauge theory of gravity in four dimensions, I have a set of tetrads $\{ e_\...
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Do retarded potentials imply homogenous solution?

I am having trouble reconciling the retarded potentials, with a possibility for a background homogenous solution to the EM field to exist. In the Lorenz gauge $$\nabla \cdot \vec{A} = - \mu_0 \...
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Dimension of moduli space for SQCD

We are in $\mathcal{N}=1$ SUSY. Consider massless SQCD with gauge group $SU(N)$ and $F$ flavours. The quarks superfields $Q$ and $\tilde{Q}$ are $F\times N$ and $N\times F$ matrices respectively and ...
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Coulomb gauge with $\rho = 0$ implies Lorenz gauge?

Maxwell equations take the form: $$\nabla^2 \phi + \frac{\partial}{\partial t} \nabla \cdot \vec{A}= - \frac{\rho}{\epsilon_0}\qquad (\nabla^2 \vec{A} - \mu_0\epsilon_0\frac{\partial^2 \vec{A}}{\...
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Is Galilean boost actually a gauge transformation?

In elementary physics, it is well-known that the Newton's law $$\vec{F}=m\vec{a}$$ is invariant under Galilean transformations. However, Galilean relativity is not introduced in details in ordinary ...
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What is the Mathematical description of Weak Interaction at low energies?

Introduction When I started to study gauge theory the mathematical road map seemed to be quite "simple". After all the concepts and notions about principal the differential geometry of fibre ...
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Functional integral for unconstrained superfields

Context In this paper by Srivastava (also in his book "Supersymmetry, Superfields and Supergravity"), he proposes the functional integral for a chiral superfield $\Phi$. In order to work ...
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Reduction of the gravity gauge from various groups

As a gauge theory, the classic reduction for gravity is from the frame bundle to the Lorentz group, \begin{equation} GL(4) \to O(3,1) \end{equation} The associated configuration space of that ...
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The constraint commute with Hamiltonian in Gauge theory

When canonical quantizing gauge theory, we find that the canonical momentum corresponding to $A_0$ vanish since the Lagrangian contains no $\dot{A_0}$ . Thus we need to choose a gauge, for example, $...
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Translating an $\mathcal{N}=2$ quiver into an $\mathcal{N}=1$ one

I am quite new to quivers and I was wondering what does the $\mathcal{N}=2$ quiver (in 4d SUSY) look like in $\mathcal{N}=1$ language? I know that the $\mathcal{N}=2$ vplet gives an $\mathcal{N}=1$ ...
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"Correct" gauge for Chern-Simons terms in 5d?

Consider 5d Einstein-Maxwell-Chern-Simons gravity with action $$S=\frac{1}{16\pi G}\int d^5x\sqrt{-g}\left[R-\frac{1}{4}F_{\mu\nu}F^{\mu\nu}-\frac{1}{12\sqrt{3}}\frac{\epsilon^{\mu\nu\rho\sigma\lambda}...
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Parametrization of classical moduli space for SUSY QED

A bit of context I'm following Bertolini's notes on SUSY and in section 5.3.1 he claims that, for a SUSY theory without superpotential, i.e. in which the $D$-flat directions coincides with the moduli ...
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$SU(2)$ comparator in Peskin & Schroeder

When Peskin and Schroeder build the comparator for a local $SU(2)$ (chapter 15.2), they say that near $U=\mathbb{I}$ any $2\times 2$ unitary matrix can be expanded in terms of the Hermitian generators ...
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$SU(N)$ gauge theory in black hole background

Assume you have standard $SU(N)$ gauge theory in a (non-asymptotically flat) black hole background (i.e., near the center of the black hole). Given the extreme pressure and temperature, I assume that ...
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Yang-Mills field-strength 2-form and exterior gauge-covariant derivative

I think that my problem is not having a formal definition of how the exterior covariant derivative works. What I know is that the exterior covariant derivative $D_A$ is defined as a generalization of ...
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What is the correct domain of integration for the index of instantons? - $\mathbb{R}^4$ or $S^4$?

I posted the original question on Math SE but it seems like a more appropriate question for Physics SE: https://math.stackexchange.com/q/4417225/ In calculating the instanton solutions for $SU(2)$ ...
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Is there any experimental test of the scattering involving Aharonov-Bohm effect?

I'm reading the paper "Significance of Electromagnetic Potentials in the Quantum Theory", Y. Aharonov and D. Bohm,Phys. Rev. 115, 485, and I wonder if there is any experimental test probing ...
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The choice of gauge seems has contradiction

Suppose I have a quantum object, inside it the electric field distribution is $\vec{E}(\vec{r})$, with this field we can obtain the scalar potential $\phi(\vec{r})$, a charged particle in this object ...
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Are covariant derivative on associated bundles exterior covariant derivatives?

The gauge covariant derivative we encounter in gauge theory $D\psi = d\psi + A\wedge \psi$ is a covariant derivative on the associated vector bundle, right? Here $\psi$ is the matter field, $A$ the ...
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How to reconcile two different expressions for the Noether current?

In A Modern Introduction to Quantum Field Theory by Maggiore (as well as in my quantum field theory course), the Noether current for an internal symmetry is found to be $$j^{\mu}=\frac{\partial\...
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Do internal symmetries always leave the Lagrangian strictly invariant?

In order for the action to be invariant under a transformation, the Lagrangian can change by a total derivative. However, for internal symmetries (where the fields transform but not the coordinates), ...
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What is / why the fiber bundle connection one-form from a physics point of view?

Take the Yang-Mills gauge theory for example. Gauge field $A$ is the pullback of the connection one-form to the base manifold. Other concepts of gauge theory also find their definition in fiber ...
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Quantized periods in electromagnetic duality path integral

In John McGreevy's notes (page 64 of https://mcgreevy.physics.ucsd.edu/w21/2021W-239-lectures.pdf), he describes a path integral derivation of electromagnetic duality for $p$-form gauge fields. The ...
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Existence of the Coulomb gauge

In reading about the Coulomb gauge, my mind seems to have painted itself into a corner. For, lets assume that Maxwells equations for the physics of the problem are solved by the magnetic vector ...
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Stückelberg mechanism and the axion

In the so-called Stückelberg mechanism we have the BF term $$ \sim \int m\; B_2\wedge F ~, $$ where the field $B_2$ is a 2-form and $F$ is the field strength arising from a $U(1)$. The Stückelberg ...
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Why do we describe gauge fields by connections?

Let $\pi:P\rightarrow M$ denote a principal $G$-bundle, where $M$ is thought of as some spacetime and $G$ is an appropriate group (such as $\mathrm{U}(1)$ or $\mathrm{SU}(2)$). I want to understand ...
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Do the retarded potentials satisfy the Lorenz Gauge condition?

Every source I have ever seen derives the retarded and advanced potentials by finding the Green's functions of the inhomogeneous Lorenz gauge conditions, and I have always thought that any linear ...
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