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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27 views

Is comoving coordinate a gauge choice?

Consider the Roberston Walker metric in 4D, $$ds^2 = -dt^2 + a^2(t) \left( \frac{dr^2}{1-kr^2} +r^2 d\Omega^2_2 \right)$$ In a lot of papers when they consider the collapse of some matter (e.g. dust), ...
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309 views

EM vector potential

We can write the electromagnetic field tensor as $$\begin{bmatrix} 0 & -E_x/c & -E_y/c & -E_z/c \\ E_x/c & 0 & -B_z & B_y \\ E_y/c & B_z & 0 & ...
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2answers
121 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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2answers
627 views

Vector potential of a solenoid in the Coulomb gauge

I understand the usual argument for calculating the vector potential outside of a solenoid of radius $R$ with $n$ turns per unit length carrying current $I_0$ using $$ \oint \mathbf{A} \cdot d \mathbf{...
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2answers
1k views

A question on gauge fixing

As I understand it, a physical theory that has a gauge symmetry is simply one that has redundant degrees of freedom in its description, and as such, is invariant under a continuous group of (in ...
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1answer
115 views

PDFs expressed through matrix elements of bi-local operators

Extracted from 'At the frontier of ParticlePhysics, handbook of QCD, volume 2', '...in the physical Bjorken $x$-space formulation, an equivalent definition of PDFs can be given in terms of matrix ...
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344 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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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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25 views

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
137 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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1answer
29 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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2answers
326 views

Can the Coulomb gauge and the Lorenz gauge be satisfied simultaneously?

The Coulomb Gauge: $\nabla \cdot A=0\\$ The Lorenz Gauge: $ \nabla \cdot A= { \mu }_{ 0 }{ \epsilon }_{ 0 }\frac { \partial V }{ \partial t }$ Can both of these gauges be satisfied for some ...
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1answer
99 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
37 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
54 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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1answer
213 views

Locality in the coulomb gauge of classical electrodynamics

In the coulomb gauge, the equations that describe the dynamics of $\Phi$ and $\vec{A}$ simplify to: $$ \Delta \Phi = - \frac{\rho}{\epsilon_0} \\ \Delta \vec{A} - \frac{\partial_t^2}{c^2} \vec{A} = - \...
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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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1answer
142 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
473 views

Gauge fixing with vector potential: Coulomb gauge

There is something I would like to clarify with gauge fixing. In E.M, we can introduce the potential vector. As $div(\vec{B})=0$ we know that we can write $\vec{B}=\vec{curl}(\vec{A})$. But as $\...
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2answers
92 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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4answers
152 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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1answer
249 views

Delta function conversion into gauge-fixing Lagrangian in the path integral

So, I am at the moment working on gauge-fixing a path integral. The procedure involves adding a delta function $\delta g$ to the path integral (together with the faddeev-popov determinant, but that is ...
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1answer
53 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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2answers
1k views

Showing that Coulomb and Lorenz Gauges are indeed valid Gauge Transformations?

I'm working my way through Griffith's Introduction to Electrodynamics. In Ch. 10, gauge transformations are introduced. The author shows that, given any magnetic potential $\textbf{A}_0$ and electric ...
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21 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
41 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
65 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
84 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
54 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
161 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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2answers
330 views

Equivalence between Lorenz gauge and continuity equation

I want to show that the Lorenz gauge condition$$ \nabla\cdot \mathbf{A} + \frac{1}{c^2}\frac{\partial\Phi}{\partial t}~~=~~0 \,,$$where $\mathbf{A}$ and $\Phi$ are the vector and scalar potential of ...
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1answer
616 views

Residual Gauge Freedom [closed]

How are we still left with one Residual Gauge Freedom in the choice of Electromagnetic Potential after having already exploited the Gauge Freedom once. As is mentioned in Halzen and Martin Section 6.9....
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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
46 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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0answers
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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3answers
3k views

Why can the divergence of vector potential be anything?

Purcell in his book was deriving the vector potential $\bf A$ using $\text{curl}\;(\text{curl}\; \mathbf A)= \mu_0 \mathbf J\; .$ After some algebra, he came to this: $$-\frac{\partial^2 A_x}{\...
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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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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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123 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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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
55 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
238 views

Is Feynman gauge reduce always physical gauge?

Is Feynman gauge reduce always physical gauge? I heard in QCD, Feynman gauge does not always give correct physics. The lecture says, "Feynman gauge gives physical gauge, if the theory contains ...
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1answer
47 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 ...