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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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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 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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1answer
56 views

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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Can we use discrete symmetry in order to generate neutrino mass in two higgs doublet model?

It is seen that an u(1) symmetry is generally used to explain the seesaw mechanism for neutrino mass in 2HDM.it is used because the theory then naturally predicts the existence of a right handed ...
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1answer
62 views

What is the physical interpretation of the derivative of a particle field?

I am learning quantum field theory, specifically the quantization of the electromagnetic field. We have this Laplacian $$ \mathcal{L} = -\frac{1}{2} \partial_\mu A_\nu \partial^\mu A^\nu -j_\mu A^\mu $...
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1answer
25 views

Is there any experiment going on to test the TWO HIGGS DOUBLET MODEL?

We know that the two higgs doublet model which is a beyond standard model theory predicts five higgs bosons.Is there any experiment that is going on to test this theory and if so have they found any ...
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41 views

Failing to show $\xi$-gauge-independence in an abelian Spontaneously Broken Gauge Theories (SBGT)

I am studying the following paper: Appelquist, Carazzone, Goldman & Quinn, Renormalization and Gauge Independence in Spontaneously Broken Gauge Theories, https://doi.org/10.1103/PhysRevD.8.1747 ...
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1answer
58 views

How do you compute the stress-energy tensor for electromagnetism + gauge fixing term?

I want to compute the stress-energy tensor for the following Lagrangian: $$\mathcal{L} = -\frac{1}{4} F_{\mu \nu} F^{\mu \nu} - \frac{1}{2\xi} (\nabla_\mu A^\mu)^2$$ but I'm struggling with the gauge-...
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Can the Fock-Schwinger (radial) gauge condition be written as momentum space divergence?

The Lorenz Gauge can be written (in QED) as $\partial^{\mu}A_{\mu} = 0$ or equivalently as $p^{\mu}A_{\mu} = 0$. The Fock-Schwinger gauge is similar: $x^{\mu}A_{\mu} = 0$. Can it be written ...
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25 views

Induced magnetic field in conducting sphere

The last day the teacher solved a problem and I did not follow all of his assumptions. We have a homogeneous conducting sphere in a magnetic field $$\vec{B}=B_0e^{i\omega t}\vec{e_z}$$. This applied ...
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29 views

Why do we need the two higgs doublet model? [duplicate]

Why do we add an extra doublet to the two higgs doublet model?I mean what are the conditions due to which we had to add an extra doublet. What are the limitations with only one doublet and how 2HDM ...
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16 views

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
41 views

Question about the Lorenz gauge in classical electrodynamics

The Lorenz gauge is the gauge such that $$\nabla \cdot \mathbf{A} = -\mu_0\epsilon_0\frac{\partial\Phi}{\partial t}.$$ This condition dictates what $\lambda$ is in $$\mathbf{A}' = \mathbf{A} + \nabla \...
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1answer
107 views

Why can we pick the divergence of the vector potential? [duplicate]

I'm aware that the vector and scalar potential in E&M can be modified using a function $\lambda(t)$ in the following way: $$\mathbf{A}' = \mathbf{A} + \nabla\lambda,\;\; \textrm{ and } \;\;\Phi' =...
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1answer
59 views

Dependence of BRST Quantization on the Choice of Gauge-Fixing Function

There is a point which confuses me about BRST procedure. One shows that, if we define physical states as the ones that are annihilated by BRST charge $Q$, the scattering amplitudes don't depend on ...
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1answer
44 views

Determine electromagnetic potentials that satisfy Coulomb and Lorenz gauge condition

In our physics lecture, we did the following example of constructing potentials $\vec A$ and $V$ that supposedly satisfy both the coulomb ($\nabla \vec A=0)$ and the lorenz condition $(\nabla \vec A+ \...
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Getting $h_x, h_y, h_z$ Components of Hamiltonian after Gauge Transformation

In Fruchart et al.'s An Introduction to Topological Insulators, the Bloch Hamiltonian for a two-band insulator is given in the general form $ H(k)= $ \begin{bmatrix} h_0+h_z & h_x-i h_y \\ ...
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1answer
149 views

How many degrees of freedom in a massless $2$-form field?

Consider the Kalb-Ramond field $B_{\mu\nu}$ which is basically a massless $2$-form field with the Lagrangian $$ \mathcal L = \frac{1}{2}P_{\alpha\mu\nu}P^{\alpha\mu\nu}\,, $$ where $P_{\alpha\mu\nu} \...
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1answer
41 views

Field intensity for electric field and vector potential

In general, the intensity of an electric field is given by $$ I = \frac{c\epsilon_0}{2}E_0^2 $$ where $E_0$ is the peak amplitude of the electric field. Let's say we have an electric field $$ E(t) = ...
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37 views

Magnetic flux changed by gauge transformation

This occurred to me when I was reviewing the Laughlin argument. Suppose a gauge transformation $A\rightarrow A+\nabla{\theta}$, where $\theta$ is the angle defined in a closed loop. When integrating ...
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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
81 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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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
221 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
58 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
68 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
81 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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1answer
69 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
44 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
57 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
47 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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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
243 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
63 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
91 views

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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112 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
79 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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1answer
104 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
37 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
108 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
454 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
208 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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122 views

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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123 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
168 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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0answers
34 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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0answers
60 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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2answers
151 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 ...