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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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What is the way to express Yang-Mills symmetry groups without gauges?

Given a Yang-Mills theory such as $SU(3)$ which has 8 gluons. After we gauge-fix this theory, it no longer has $SU(3)$ guage symmetry. Yet, we still use the group constants and the 8 types of gluons ...
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1answer
28 views

How to show the that Lorenz gauge is true given that the scalar and the magnetic vector potentials are not unique?

So I understand that we select the divergence of A (magnetic vector potential) to be: $$\frac{1}{c^2}\dot{\phi} + \nabla\cdot\vec{A} = 0.$$ The Lorenz gauge (1). because of the symmetries in ...
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1answer
93 views

Why is the gauge-fixing condition squared in the QED Lagrangian?

Consider the free Maxwell Lagrangian: $$L= -\frac{1}{4}F_{\mu\nu}F^{\mu\nu}. $$ As we know, the gauge symmetry $A_{\mu} \rightarrow A_{\mu}+\partial_\mu \lambda$ must be fixed when quantizing the ...
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1answer
33 views

Quantisation of gauge theory with minimal coupling

I have a question on the quantization of the gauge theory with minimal coupling term. What I understand is that if one is given an action $$ S=-\int d^4 x \frac{1}{4}F^2 \tag1 $$ Since this action has ...
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2answers
53 views

What happens to the symmetry after gauge fixing?

Given a theory with gauge symmetry. After gauge fixing where does the symmetry go? Does the gauge symmetry turn into a global symmetry? For example there is a way to quantize fields theory with BRST ...
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2answers
78 views

Lorenz Gauge Condition in Helmholtz equation

I do not understand why we can apply the Lorenz Gauge Condition in Helmholtz equation. What is its physical meaning? Any help is appreciated. $\nabla\cdot \vec{A} + \mu_0\varepsilon_0\frac{∂\phi}{∂...
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1answer
42 views

How does the Lorenz Gauge condition lead to four wave equations?

The 1972 book by L. Eyges's, The Classical Electromagnetic Field, on p. 184, in $\S$11.7, Integral Forms of The Potential, the statement "We now turn to the problem of finding $\mathbf{A}$ and $\...
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2answers
88 views

How does gauge-fixing really work?

Leaving technical issues like Gribov copies and residual gauge freedom aside, how do gauge fixing conditions like the Coulomb condition \begin{equation} \partial_i A_i =0 \end{equation} or the axial ...
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1answer
52 views

Why does Coulomb gauge condition $\partial_i A_i =0$ pick exactly one configuration from each gauge equivalence class?

There are infinitely many configurations of a vector field $A_\mu$ that describe the same physical situation. This is a result of our gauge freedom $$ A_\mu (x_\mu) \to A'_\mu \equiv A_\mu (x_\mu) + \...
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4answers
138 views

Why does Lorenz gauge condition $\partial_\mu A^\mu =0$ pick exactly one configuration from each gauge equivalence class?

For a vector field $A_\mu$, there are infinitely many configurations that describe the same physical situation. This is a result of our gauge freedom $$ A_\mu (x_\mu) \to A'_\mu \equiv A_\mu (x_\mu) + ...
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0answers
19 views

Time Average Spin Angular Momentum

I’m a bit confused about time averages in electromagnetism using complex amplitudes. Specifically about the angular momentum of the fields- the spin part is proportional to $\bf{E} \times \bf{A}$. In ...
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1answer
39 views

Gauge fixing of Polyakov Action

In the Gauge fixing of Polyakov action we do general coordinate transformation where we take the transformation stated below $$h_{\alpha\beta} = e^{\phi(\sigma)}\eta_{\alpha\beta}.$$ But here the ...
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24 views

Does the temporal gauge condition uniquely determine a gauge in case of non-Abelian gauge theory?

For a $U(1)$-gauge theory, we can fix $A_0 = 0$ by choosing a temporal gauge. Can we do the same for all of the gauge components of the $SU(2)$ gauge field, i.e., $W^a_0 = 0$ for $a \in \{1,2,3\}$? ...
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1answer
64 views

Gauge anomaly in Polyakov string and Faddeev-Popov method

I am currently trying to gain a better understanding of the gauge fixing procedure used in chapter 5 of David Tong's notes. Since the central charge of the Polyakov action for, say, the bosonic ...
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1answer
140 views

Gauge transformation for Bloch waves?

I have seen in many places saying a gauge transformation transform the Bloch wave function as $\psi_{nk}\to e^{-i\phi_n(k)}\psi_{nk}$. However I don't quite understand how it is related to the "gauge ...
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1answer
79 views

Which form of Lagrangian should I choose for uniform magnetic field?

Here's the problem and corresponding question. Let's consider a uniform magnetic field $\vec{B}=B_0\hat{z}$. Looking for the solution of vector potential satisfying $\vec{B}=\vec{\nabla}\times \vec{A}...
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1answer
52 views

How Gupta-Bleuler condition implies $(a_p^3-a_p^0)| \phi \rangle=0$?

Gupta-Bleuler condition is $$\partial^\mu A_\mu^+ | \phi \rangle=0\tag{6.54}$$ where $$A_\mu^+= \int\frac{d^3\mathbf p}{(2\pi)^3 \sqrt{2|\mathbf p|}} \sum_{\lambda=0}^3 \epsilon^\lambda_\mu a_p^\...
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0answers
160 views

Difficulty to understand a chain of equalities

If we start with a functional or integral action \begin{equation} \mathscr{F}(\boldsymbol{\mathcal{A}})=\iiiint_{D} L\Biggl(x_\nu, \mathcal{A}_\mu, \frac{\partial \mathcal{A}_\mu}{\partial x_\nu}\...
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53 views

Conservation laws and Gauge transformations

I am studying gauge transformations, and my professor asked me: "Can the potentials obtained by the Lorenz gauge be considered physical quantities?" I assumed that "physical quantity" is ...
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65 views

Has the conjecture of Guillemin-Sternberg been proven for relevant physics cases?

From a working physicist's perspective, the conjecture of Guillemin-Sternberg (and its generalisations) seems to state in a highly technical manner that quantization commutes with gauge-fixing. In ...
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1answer
48 views

What if the two Higgs doublet model is proved right? [closed]

Two higgs doublet model predicts five higgs bosons. If five higgs will be found then how it will impact the known physics?
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1answer
38 views

How a discrete z2 symmetry removes flavour changing neutral current from Two Higgs Doublet Model?

By applying a discrete Z2 symmetry to the theory of Two Higgs Doublet Model it is ensured that fermions of one type couples to only one doublet. But how FCNC is removed by doing so? Because if all ...
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2answers
109 views

Gauge fixing, invertibility and Green's functional

consider the photon in QED and the corresponding EOM of its Green's functional in k-space: $$(k^\mu k^\nu-k^2g^{\mu\nu})\Delta_{\nu\rho}(k)=i\delta^\mu_\rho.$$ Now, I understand that $U^{\mu\nu}(k):=...
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33 views

What happens to large gauge transformations in gauges different from the temporal gauge?

There are already several questions regarding the meaning and definition of large gauge transformations. Discussions of large gauge transformations typically only happen in the context of the ...
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22 views

Gauge Fields from Compactified Gravity

I encountered compactifying a 5D black string along an extra dimension in Natsuume's AdS/CFT text. Upon compactification, the thermodynamics of a 4D black hole may be identified with the 5D black ...
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1answer
77 views

What is a gauge (for someone who has not studied gauge theory)? [duplicate]

I am taking a Quantum Mechanics II course and we were studying the relativistic corrections to the hydrogen atoms in perturbation theory. I was looking at the assignment, and a question is as follows: ...
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0answers
63 views

Anderson-Higgs Mechanism

Consider an abelian gauge field coupled with a complex field: $$\mathcal{L}=-\frac{1}{4}F_{\mu\nu}F^{\mu\nu}+(D\varphi)^\dagger D\varphi+\mu^2 \varphi^\dagger\varphi-\lambda(\varphi^\dagger\varphi)^2.$...
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122 views

Explicit counting of gauge field degrees of freedom

Consider a connection on a principal $U(1)$-bundle $A_\mu$ over the flat base manifold $M_4$. The action of the theory is described in terms of the curvatures of such connection coupled to some source ...
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0answers
27 views

Fields and gauge transformations vanishing at infinity

I find that, in field theory, it is very often assumed that the fields (classical) vanish at infinity. The same assumption is also applied to gauge transformations, for example, when saying that the ...
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1answer
47 views

Landau levels in symmetric gauge

On Shankar’s Quantum Many body page 394 it says for one electron in a magnetic field, ignoring spin, $$H_0=\frac{(\bf{p}+e\mathbf{A})^2}{2m}$$ $$e\mathbf{A}=-\frac{\hbar}{2l^2}\hat{z}\times \mathbf{...
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38 views

Why is the Coulomb Gauge enough to fix extra degrees of freedom?

In classical electrodynamics, we have after the Coulomb gauge is applied: $$ \Delta U = -\frac{\rho}{\epsilon_0} $$ $$ \Box \vec{A} = \mu_0 \vec{j}-\frac{1}{c^2} \vec{\nabla} \frac{\partial U}{\...
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1answer
52 views

Showing $ \nabla \cdot \mathbf A = 0$ using integral formula

In Coulomb gauge the vector potential is chosen so that $ \nabla \cdot \mathbf A = 0$ and we find $$ \nabla^2 \mathbf{A}=-\mu_0 \mathbf j $$ The solution to which is $$ \mathbf A(r) = \frac{\mu_0}{4\...
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1answer
42 views

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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34 views

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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0answers
31 views

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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0answers
45 views

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
64 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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0answers
19 views

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
64 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
32 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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0answers
43 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
85 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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0answers
34 views

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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0answers
35 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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0answers
35 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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0answers
25 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
50 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 \...
4
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1answer
136 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
72 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
51 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+ \...