Questions tagged [gauge]

Use this tag to discuss gauge-fixing conditions, as in the phrase 'choosing a gauge', such as, e.g. the Lorenz gauge, Coulomb gauge, Feynman gauge, Landau gauge, axial gauge, temporal gauge, light cone gauge, etc.

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Nickel gauge factor and why is it so quirky?

Hi so I've been researching the piezo-resistance effect and experimenting with finding different metals' gauge factors by applying stress on a wire and measuring the change in resistance however I can'...
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Derivation of $\mathbf{J}_{l}$ and $\mathbf{J}_{t}$ in the Coulomb gauge in Jackson's EMT book

So the vector potential $\mathbf{A}$ satisfies the following equation $$ \begin{equation} \nabla^2\mathbf{A} - \frac{1}{c^2}\frac{\partial^2 \mathbf{A}}{\partial t^2} =-\mu_o\mathbf{J} + \frac{1}{c^2}...
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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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Gauge anomalies?

Why are gauge anomalies so important for any model? Secondly, any model has to respect the gauge anomalies cancellation requirement? If this isn't true, then why does one check their model to look ...
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Does $\xi$ invariance in $R_\xi$ gauges imply gauge invariance?

Often in QFT calculations, a $R_\xi$ gauge fixing term $$ \mathcal{L}_{GF} = \frac{1}{2\xi}(\partial_\mu A^\mu) $$ is used, with $\xi$ left arbitrary. Any gauge invariant quantity must then be $\xi$ ...
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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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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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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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Calculating the electric potential in the Lorenz gauge

It has been a while since I have done any electromagnetism, and at one point I knew how to do this but for the life of me can't figure this out. The problem is as follows, if we have a time dependent ...
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Divergence of the vector potential in Lorenz gauge, in magnetostatics

If we consider a localized current distribution and the following natural boundary condition : $\vec A(\vec r \rightarrow 0)$ for $\vec r \rightarrow \infty$ If $$\vec A(\vec r)=\int_V G_0(\vec r, \...
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Conformal tranformation on string coordinates in order to fix static gauge

Some time ago I made this post on Phys.SE. The post was about finding classes of backgrounds that allows static gauge in Polyakov action by the use of its residual symmetry. Besides I did not found ...
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A relationship between the proof of a renormalizability and gauge fixing conditions?

I already know that QCD is renormalizable in several gauges, including the $\xi$ gauge and the background field gauge. That is, the divergence of the quantum effective action is limited by symmetry, ...
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Transforming potentials to the appropriate gauge

In my script I had the following example of gauge transformation (when $\rho=0$, $\vec j(\vec r,t)=0)$: \begin{gather} \phi(\vec r)= -\frac{\partial f(\vec r,t)}{\partial t}, \\ \vec A(\vec r,t)= -\...
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Transforming the potentials that satisfy Lorenz & Coulomb gauge to potentials that satisfy only Lorenz gauge

If $\vec E(\vec r,t)=\vec E_0sin(\vec k \vec r- \omega t)$ and also that $\rho(\vec r,t)=0$ and $\vec j(\vec r,t)=0$ I was asked to find $\vec A(\vec r,t)$ and $\phi (\vec r,t)$ which satisfy both the ...
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Lorenz Gauge different definitions

For the lorenz gauge we can either write: $$\nabla \vec A(\vec r,t)+\frac{1}{c^2}\frac{\partial \phi(\vec r,t)}{\partial t}=0$$ If we also consider the following invariant transformations: $$\vec A(\...
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Coulomb Gauge misunderstanding

If we have $\vec A(\vec r,t)$ and $\phi (\vec r,t)$ and we make the following gauge transformations: $$\vec A(\vec r,t)'= \vec A(\vec r,t) + \nabla f(\vec r,t)$$ $$\phi(\vec r,t)'=\phi(\vec r,t) - \...
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Harmonic coordinates in General Relativity

I was going through chapter 10 of Wald's book on GR. The part I am reading concerns the harmonic gauge: \begin{equation} H^\mu\equiv \Box x^\mu=0. \end{equation} In eq. (10.2.34) he gives the Ricci ...
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2 answers
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"One-parameter" gauge transformation

In my advanced classical physics course, it was stated that the electromagnetic field strength tensor $F_{\mu\nu} = \partial_{\nu}A_{\mu} - \partial_{\mu}A_{\nu}$ is invariant under "one-...
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Divergence of magnetic vector potential is zero

Given the potential $$ \vec{A}=\frac{\mu_{0}}{4 \pi} \int_{V}^{\prime} \frac{\vec{J}\left(r^{\prime}\right)}{R} d v^{\prime} $$ where $\vec{J}$ is the stationary current density vector. I want to ...
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Is Weyl gauge together with Coulomb gauge a possible choice?

I am working in the Weyl gauge with an action in euclidean signature (so the Lagrangian is a Hamiltonian): \begin{equation} S=-\frac{1}{96\pi^2}\int_{\mathbb{R}^4} d^4 x\,\text{Tr}\left( E_i \cdot ...
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Gauge choice and validity of Magnetic vector potential for an infinitely straight wire

Consider an infinitely thin, infinitely long wire, Using the standard formula for the magnetic vector potential, we obtain the result that the magnetic vector potential is infinity,( with no variables)...
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Lorenz gauge for non-homogenous wave equations in vacuum

If we do the following gauge trasformation for magnetic potential and electric potential : $$\vec A(\vec r,t)'=\vec A(\vec r,t) + \nabla f(\vec r,t)$$ $$\phi((\vec r,t)'=\phi((\vec r,t) - \frac {\...
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Gauge fixing terminology (math terms) [duplicate]

In the majority of the sources I've read regarding gauge fixing, the authors sometimes use (IMHO) a vague terminology. Let's take the case of the magnetic vector potential $\vec{A}$ defined as $$ \vec{...
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The residual gauge symmetry of Yang-Mills theory after Wick rotation

I am a bit puzzled by a statement in this question here. In particular, the claim that the residual gauge symmetry in Yang-Mills theory disappears upon Wick rotation to the Euclidean theory. For ...
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Ehrenfest theorem: On which classical circle can we find the electrons in an homogenous magnetic field?

In the French wiki article about the Ehrenfest theorem I found these formulas. $${\displaystyle {\frac {\mathrm {d} }{\mathrm {d} t}}\langle {\hat {x}}\rangle ={\frac {1}{m}}\langle {\hat {p}}\rangle }...
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The $D_{00}$ component of the photon propagator in the Feynman and Coulomb gauges

I am trying to understand some derivations involving the photon propagator, and I am having a lot of trouble with expressions in different gauges and also with terminology in general. Here is what I ...
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1 answer
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Local order parameter for confinement in gauge theories

I would like some help clarifying what Zinn Justin is saying in his book "Quantum Field Theory and Critical Phenomena" p.805 on detecting confinement of gauge theories. In particular, I ...
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Gauge fixing of non-Abelian interactions [duplicate]

If we consider a non-Abelian potential $A_{\mu}=A^{a}_{\mu}T^{a}$ of a general non-Abelian group $G$, satisfying the property $F_{\mu\nu}=\partial_{\mu}A_{\nu}-\partial_{\nu}A_{\mu}+[A_{\mu},A_{\nu}]=...
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Pure gauge of non-Abelian interactions [duplicate]

if we consider the $U(1)$ potential $A_{\mu}(x)=\partial_{\mu}f(x)$ (i.e. $F_{\mu\nu}=\partial_{\mu}A_{\nu}-\partial_{\nu}A_{\mu}=0$), then we can perform a $U(1)$ gauge transformation $A_{\mu} \...
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GR gauge condition corresponding to isotropic coordinates

Does anybody know what kind of gauge condition I have to use in order to work in isotropic coordinates in general relativity? I ideally want a condition on a small metric perturbation (or graviton) $...
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Can a single QFT field configuration be written as a set of spinor/vector valued functions?

If a QFT state is a probability distribution over field configurations, then a single field configuration must correspond to an observable situation, right? As far as I can gather, each field ...
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The order of the time-space components of the metric tensor in post-Newtonian expansion

In the book Gravitational waves Vol.1: theory and experiment by M.Maggiore, in chapter 5, page 239, the author announces that when we expand the metric tensor by $v \over c$, the components $g_{0i}$ ...
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How to makes Coulomb gauge Fields?

it is all in this paper. i know how to makes coluomb gauge but makes coloumb gauge we designate charge distribution to satisfy gauge fix is that possible in any A_0?
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Gauge invariance of magnetic vector potential

If we go by transformation for magnetic vector potential $\mathbf{A} \rightarrow\tilde{\mathbf{A}}=\mathbf{A}-\nabla\psi$, as well as $\varphi \rightarrow \tilde{\varphi}=\varphi+\frac{\partial\psi}{\...
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Gauge invariant Green's function for a point particle

This question is a follow up to the question (Gauge invariant Green's function for electrodynamics). It is not possible to generally solve the eqution \begin{equation} \square A^{\mu}-\partial^{\...
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Quadrupole formula in TT gauge

In weak gravity limit, we can derive the celebrated quadrupole formula in Lorenz gauge $\partial^{\mu} \bar{h}_{\mu \nu} = 0$: $$ \bar{h}_{ij} = \frac{2G}{r}\frac{d^2}{dt^2}I_{ij}(t_r) $$ To get $h^{...
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Gauge invariant Green's function for electrodynamics

Varying the electromagnetic action \begin{equation} S=-m c \int d s\left(\dot{z}^{2}\right)^{\frac{1}{2}}-\frac{e}{c} \int d s A_{\mu} \dot{z}^{\mu}-\frac{1}{16 \pi c} \int d^{4} x F_{\mu \nu} F^{\mu \...
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In the Kitaev honeycomb model, is it possible to get a ground state that is completely 'unphysical' when working with Majorana representation?

Kitaev's way of exactly solving his honeycomb model described here is to describe the system using Majorana fermions, a description that introduces a lot of unphysical degrees of freedom. The up shot ...
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Gauge-fixing conditions in Einstein-Cartan gravity

What are the gauge-fixing conditions one needs to impose on the tetrad one-form $e^a$ and the spin-connection one-form $\omega^{ab}$ while working in the Einstein-Cartan formalism where both are ...
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4 votes
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Gauge symmetry of massive vector field

Consider a real massive vector field with lagrangian density $$\begin{align}\mathcal{L}&=-\frac{1}{4}(\partial_\mu A_\nu-\partial_\nu A_\mu)(\partial^\mu A^\nu-\partial^\nu A^\mu)+\frac{1}{2}m^2 A^...
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Harmonic Gauge Condition

I was recently looking at Sean Carrols notes on G.R.: https://ned.ipac.caltech.edu/level5/March01/Carroll3/Carroll6.html , where in eqn 6.37 he states $$\text{"The Harmonic Gauge Condition: $\square x^...
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2 votes
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Limitations of describing QED interactions in the Coulomb gauge?

When we work with the S-matrix operator to describe interactions between the quantized Maxwell field and a classical source or a Dirac field, are there any limitations one needs to keep in mind when ...
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1 answer
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Gauge fixing in the classical $U(1)$ gauge theory

My question concerns the gauge fixing in classical v.s. quantum $U(1)$ gauge theory. I will ask about the gauging fixing in quantum $U(1)$ gauge theory in a separated Phys-SE post. For the classical $...
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1 vote
1 answer
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Quantisation of gauge field in temporal gauge

Whenever we use temporal gauge and quantise gauge field we implement Gauss law. I have seen some papers but the point is not cleared to me that why we implement Gauss law there. Please explain this if ...
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What is wrong with my counting of electromagnetic field degrees of freedom?

When we go from the field variables $({\vec E},\vec{B})$ to the potentials $(\phi,{\vec A})$, the number of degrees of freedom describing any electromagnetic field is reduced from $6$ ($3$ components ...
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2 answers
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Section of adjoint bundle in gauge theory

I have a couple of questions on gauge theory. Considering a principal $G$-bundle $P\xrightarrow{\pi} M$, we have a connection, a local Lie algebra-valued 1-form $A$. This is the photon field, correct? ...
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Gauge fixing and transformation

given the gauge choice that div A = some value/function. i am completely fine that in the context of electromagnetism that by setting the divergence of this to be anything it has no effect on the curl ...
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2 votes
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Why the $R_{\xi}$-contribution to the Lagrangian disappears when computing physical observables?

In QED for example, you add the term $$\mathcal{L}_{GF}=-\frac{1}{2\xi}(A_{\mu}A^{\mu})^{2}$$ so you can compute the photon propagator. The question is basically, why you can compute physical ...
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Fock-Schwinger gauge in pure Yang-Mills theory and coordinate dependence of equations of motion

Let $(\Omega^\bullet (\mathbb{R}^n,\mathfrak{g}),d_A)$ be the Yang-Mills cochain complex on $\mathbb{R}^n$, where $d_A$ is the gauge covariant derivative, $d_A \circ d_A=0$. I was wondering: if we ...
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5 votes
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Gauge dependence of Feynman propagator

In QED we have the property that any gauge dependence must cancel out in physical quantities. Nevertheless Feynman rules display some gauge dependence. This is what I am a little unclear on. The ...
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