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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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QCD gluon physical polarisation sum in the three gluon vertex

In the Compton scattering quark($p_1$) + gluon ($q_1$)-> quark($p_2$) + gluon($q_2$), there is three gluon vertex contribution. If we choose the physical polarisation sum $\sum_{\lambda} \epsilon^a(\...
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1answer
60 views

Why do we impose de Donder gauge?

In the field language, a massless particle corresponds to irreducible representations of the Lorentz group. In particular, given a spin-2 massless particle, we can embed the creation and annihilation ...
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3answers
971 views

Are Maxwell's equations “physical”?

The canonical Maxwell's equations are derivable from the Lagrangian $${\cal L} = -\frac{1}{4}F_{\mu\nu}F^{\mu\nu} $$ by solving the Euler-Lagrange equations. However: The Lagrangian above is ...
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1answer
67 views

QED lagrangian: gauge fixing term

I have a question about the structure of the QED lagrangian, in particular the free photon lagrangian which is contained in it. My premise is: I only know how to exploit canonical quantization in ...
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1answer
48 views

Why is the projective symmetry group a group?

I am reading the paper from X. Wen about quantum orders and symmetric spin liquids. It can be found here: https://arxiv.org/abs/cond-mat/0107071 The Hamiltonian he is writing about looks like this: \...
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What component of the strain tensor is a strain gauge measuring in a bend test?

I am studying a bend test of a beam. The beam is set up like a 4 point bend. The force is applied at 2 locations on the top surface, and 2 locations on the bottom surface are fixed in place. It is ...
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1answer
52 views

Gauge fixing: Overcounting vs Inversion of Operator

In my studies (various books, and Lectures by Tobias Osborne) I've been told we gauge fix to stop the naive overcounting in the path integral. User @Marmot pointed out in a comment that if this was ...
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1answer
60 views

Why Coulomb gauge is a possible gauge choice?

In classical field theory we can get, that adding gradient of some scalar field to magnetic vector potential does not change the physics at all. So, we have such a symmetry: $\boldsymbol{A}\...
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34 views

Gauge fixing while preserving supersymmetry

In supersymmetric gauge theories, the vector potential is a part of a vector supermultiplet which is represented by a real superfield $V$. Expanded out in components, the Lagrangian for such a field ...
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1answer
34 views

Is any other gauge ever more useful than Lorenz gauge for practical calculations in classical EM?

Any problem in gauge theory can of course in principle be solved in any gauge (or, in the case of classical gauge theory, without using gauge potentials at all), but some gauges are much more useful ...
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1answer
49 views

Can we always choose a gauge in GR in which time is constant?

In General relativity the metric describes the curvature of 4D space-time. But due to diffeomorphism invariance, many metrics describe the same physics. Can we always choose a metric such that we can ...
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1answer
40 views

Energy in an electric field under a gauge transformation

Consider a (test) charge located at $\vec{r}(t)$ in a static electric field with potential $V(\vec{r})$. The energy for this system is given by $$E = \frac{1}{2} m \dot{\vec{r}}(t)^2 + q V(\vec{r}(t))...
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2answers
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Help with understanding the imposition of gauge conditions

Let $s$ be a positive integer and $h_{a_1\dots a_s}$ be a traceless and totally symmetric (real) field which is defined modulo gauge transformations of the form $$\delta_{\xi}h_{a_1\dots a_s}=\...
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2answers
202 views

What is the $\,\phi=0\,$ gauge called?

In electromagnetism textbooks, the gauges most often talked about are the Lorenz gauge and Coulomb gauge. Sometimes it's convenient to work in a gauge in which there is only the vector potential $\vec{...
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1answer
52 views

Quick question on choosing a gauge (E.g. Lorenz gauge)

I have been quite confused when I read about choosing a gauge. For example we have the gauge transformation $$ A_\mu\longrightarrow A_{\mu\prime}= A_\mu+\partial_\mu\alpha, $$ and we can choose any $...
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3answers
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Why does gauge invariance in electrodynamics mean that there are redundant degrees of freedom? [closed]

It is possible to choose different gauges in electrodynamics. I am familiar with two of them: Coulomb gauge and Lorenz gauge. Let us stick to the Coulomb gauge. It sets $$\nabla\cdot\vec{A}=0.$$ The ...
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1answer
73 views

What exactly are the sections in gauge theories?

In trying to understand precisely how fiber bundle theory maps to physical models, I came across this quotation: We can think of the elements of the principal bundle as generalized frames for the ...
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1answer
53 views

Commutators in Gupta-Bleuler formalism for quantization of the electromagnetic field

In the Gupta-Bleuler formalism we have for the canonical momenta $$\pi_\mu=F_{\mu0}-g_{\mu0}\partial_\alpha A^\alpha. $$ Every resource I find online say that the equal time canonical commutation ...
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Continuity equation is guage invariant for a charged particle in electromagnetic field

I know that the Schrodinger equation is gauge invariant but how to show that the continuity equation is also gauge inavariant? Any comments?
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1answer
65 views

What does the $R$ stand for in $R_\xi$ gauge?

The $R_\xi$ gauge fixing condition is a term that can be added to a Lagrangian to choose a certain gauge: $$ \delta\mathcal L = -\frac{1}{2\xi}(\partial_\mu A^\mu)^2 $$ Here, $\xi$ is the parameter ...
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1answer
31 views

How does the Lorenz gauge eliminate the scalar component of the vector field?

Wikipedia states that by using the Lorenz gauge, $\partial_\mu A^\mu=0$, we eliminate the scalar part (spin-0) of the vector potential that previously had spin-1 and spin-0 components${}^1$. However,...
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2answers
83 views

The meaning of gauge-fixing in covariant quantization of the electromagnetic field

I am having trouble wrapping my head around the idea behind the covariant quantization for the electromagnetic field that is usually done in textbooks (I'm currently following Mandl & Shaw and ...
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2answers
438 views

The location of an object is gauge dependent. Therefore, it's not measurable?

The location of an object $x$ depends on how we choose our coordinate system. If we move the zero point, $x$ also changes. However, since we have translational invariance, we can always do such shifts ...
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2answers
165 views

Gauge Invariance in Electrodynamics

I am studying Electrodynamics and I have been introduced to the concept of Gauge Invariance. This was introduced by noting that $E$ and $B$ amount to 6 six degrees of freedom and the Maxwell ...
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4answers
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Is fixing the gauge the same thing as performing a Lorentz transformation?

Let's say I have a moving charged particle, with constant velocity. Its electric field is given by (generally): $$ \mathbf{E} = -\nabla\phi - \frac{\partial \mathbf{A}}{\partial t}. $$ If I perform ...
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Conformal invariance and Diffeo - Weyl invariance

Consider a 2d Conformal Field Theory, with the metric of the underlying spacetime being $\gamma_{ab}$. I understand that we have the freedom to set $\gamma_{ab}$ to a flat form (either Euclidean or ...
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71 views

Confusion Between Associated and Principle-G-Bundles

I realize there have been similar questions on stack before, but none of them have answered what I'm after. -My question is really whether I can import wholesale everything from the principle bundle ...
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1answer
140 views

Equations of motion from Polyakov action, before choosing the conformal gauge

My question is the following: It is usual in the standard textbooks to firstly choose a gauge (usually the conformal gauge) and then extract the equations of motion from the Polyakov action by ...
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21 views

Relation between Adiabatic modes in cosmology and asymptotic symmetries

I know that adiabatic modes in cosmology has close relationship with large gauge transformations mostly discussed in asymptotically flat gravity or in gauge theory. However, there are differences and ...
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39 views

Local energy current between subsystems

Consider an isolated system, whose Hamiltonian $H$ can be decomposed as \begin{equation} H = H_A + H_B + H_C, \end{equation} where $H_A$, $H_B$, $H_C$ are the Hamiltonians of the subsystems $A$, $B$,...
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27 views

Re-expressing the Lorenz gauge condition in terms of the Faraday tensor (in curved spacetime)

I was wondering if the equation $\nabla_\mu A^\mu = 0$ could be written as a constraint equation solely on the $F_{\mu \nu}$ components. It seemed like the bulk of the problem was isolating terms such ...
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46 views

Bloch theorem in Hofstadter problem

right now I'm dealing with the Hofstadter Butterfly. Currently I'm reading and trying to understand a paper. It's about the following paper: https://arxiv.org/pdf/cond-mat/9312088.pdf. Zabrodin, ...
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139 views

Confusion on Maxwells equations and Gauge Transformations

I know a little bit about electrodynamics but I don't understand the validity of Gauge Transformations. In particular I am confused on how the theory can be consistent among different gauges, in ...
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82 views

Covariant version of the Coulomb gauge

In curved spacetime, it is possible to define the covariant version of the Lorenz gauge, going from $\partial_\mu A^\mu =0$ to $\nabla _\mu A^\mu =0$ in some curved spacetime $g_{\mu \nu}$. What is ...
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2answers
126 views

Question about the Faddeev-Popov method for gauge-fixing

The correct way to gauge-fix in a path integral is to insert the Faddeev-Popov determinant, and add a delta-functional constraint. The final action contains three contributions: a Yang-Mills (I'm ...
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Gauge-invariance of curvature perturbation in uniform density gauge

The perturbed energy conservation equation is given by $$\delta\rho'+3\mathcal{H}(\delta\rho+\delta P)-3(\bar{\rho}+\bar{P})\psi'+(\bar{\rho}+\bar{P})\nabla^2(V+\sigma)=0.$$ If we substitute in the ...
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1answer
27 views

Gauge invariance of Landau-Ginsburg model [closed]

Free energy density for Landau-Ginsburg model is given by: $$ F=\frac{1}{2\mu}(\vec\nabla \times \vec A)^2+|(\vec\nabla-ie\vec A)\phi|^2+a(T-T_c)|\phi|^2+\lambda|\phi|^4 $$ And I was trying to show ...
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71 views

Problem with the Landau gauge

I'm having a very simple problem which probably has an equally simple answer. I'm following the wikipedia article: https://en.wikipedia.org/wiki/Landau_quantization We have a uniform magnetic field ...
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3answers
271 views

What is the Lorenz condition for potentials?

I was just going through the "Electromagnetic Waves" chapter in the Classical Field Theory book by Landau. Here he mentions that they impose an auxiliary condition and it is known as the Lorenz ...
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119 views

Residual gauge fixing in Lorenz gauge

Background Let $A^{\mu}$ be a 4-potential that satisfies the Lorenz condition $$\partial_\mu A^\mu =0$$ We can make a gauge transformation $$A_\mu \to A'_\mu=A_\mu + \partial_\mu \Lambda$$ such that $...
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1answer
82 views

EM field in a vacuum in terms of potentials

I know we can express the electric field $\mathbf{E}$ and the magnetic field $\mathbf{B}$ in terms of the electric potential $\phi$ and vector potential $\mathbf{A}$: $$ \mathbf{E} = -\nabla \phi - \...
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Cutoff regularization for loop integral with massless propagators

I am using Landau gauge, so Goldstone bosons are massless. The loop integral is $\int d^4 k \frac{1}{k^2 (k+p)^2}$. Here k is the loop momentum and p is the Higgs momentum. How can one calculate this ...
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1answer
74 views

Vector Identity using Coulomb Gauge in Stancil and Prabhakar's 'Spin Waves'

I'm working through Stancil and Prabhakar's 'Spin Waves', and am stuck with a vector identity which I am not sure how the authors have justified. On page 34, we adopt the use of a scalar potential $\...
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1answer
84 views

Do we fix divergence of the vector potential $A$, because $\nabla \cdot \nabla \psi \ne 0$?

Because $\nabla \times \nabla \psi = 0$, we can transform the vector potential $A \longmapsto A + \nabla \psi$, without changing the magnetic field. Is the reason we specify $\nabla \cdot A$ in the ...
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202 views

Trace-reversed EFE and linearized gravity

I have a question about the linearized Einstein Field Equations, and in particular about the Newtonian limit. It goes as follows. If one uses the trace-reversed form of the EFE for the 00-component ...
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370 views

Counting massive degrees of freedom after gauge fixing

Consider the theory of scalar QED with the Lagrangian $$\mathcal{L} = - \frac14 F^{\mu\nu} F_{\mu\nu} + (D^\mu \phi)^* (D_\mu \phi) - m^2 \phi^* \phi \tag{1}$$ where $\phi$ is a complex scalar field ...
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Confusion about rewriting the Lagrangian in Unitary Gauge

So I was reading through these lecture notes (The Standard Model Higgs Boson - UvA Particle Physics II) on the Higgs mechanism and there’s one line I can’t make sense of. After removing all terms ...
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1answer
86 views

Boundary Conditions giving Gauge Transformation a Physical Meaning?

I am currently reading Robert Laughlin's Nobel lecture. In the part where he uses gauge invariance to explain integer quantization of the Hall conductivity, he has a 2D rectangular surface which is ...
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39 views

(In practice) Is a gauge choice just a substitution we use to simplify an equation?

When working in linearised gravity (and PPN formalism), is choosing a gauge essentially choosing an identity that we can substitute into the equation of motion (to help simplify it)? By that, I mean ...
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41 views

Necessary and sufficient conditions for a gauge in Hamiltonian dynamics

Disclaimer. I have only Russian version of the article I refer below. Therefore the text I cite may be not correct. By the way, here is the reference on the article in my book: Dirac P.A.M., 1958, ...