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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How to apply the Faddeev-Popov method to a simple integral

Some time ago I was reviewing my knowledge on QFT and I came across the question of Faddeev-Popov ghosts. At the time I was studying thеse matters, I used the book of Faddeev and Slavnov, but the ...
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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 ...
4
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2answers
150 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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439 views

Gauge invariance and the unitarity

I want to discuss the relation between the unitarity and the gauge invariance. Suppose we have for simplicity an abelian gauge theory (say, EM theory). We want to quantize it in terms of 4-potential $...
4
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0answers
972 views

Why not use the Weyl gauge?

In E&M in Minkowski space, the Lorenz and Coulomb gauges are typically used since they make things vastly simpler. On a curved background, Maxwell's equations (without sources) can be written as: ...
3
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0answers
189 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 ...
3
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164 views

Gauge invariance in General relativity and Classical Electrodynamics

As I understand from popular talks that gauge invariance is a problem in finding out exact solutions of Einstein's field equations (apart from the complication that it is non-linear), and gauge fixing ...
2
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1answer
71 views

Path integral formulation of an Abelian Field Theory, unclear identity

TL;DR: How exactly does one come to this identity $$\int\mathcal{D}G(A^\alpha)\delta(G(A^\alpha)) = \int\mathcal{D}\alpha(x)\delta(G(A^\alpha)) \mathrm{det}\left(\frac{\delta G(A^\alpha)}{\delta\...
2
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165 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}\...
2
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70 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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55 views

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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218 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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270 views

Ghost Fields in Abelian and Non-Abelian gauge theories

I have some questions about ghost fields in QED and in a non Abelian gauge theory: Does the fact that ghosts and photons are decoupled depend on the choice of the gauge-fixing function? In the Lorenz ...
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92 views

Axial gauge in lattice gauge theories with matter fields

I am studying the lattice gauge theory coupled with matter (Higgs) fields in the 1979 Fradkin-Shenker paper (https://inspirehep.net/record/132906). Taking the matter fields $\sigma$ and the link ...
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36 views

Relevance of Gauge Transformations in Physical Interpretations of a System

In the simple example of a stationary electric field (and some other quantum mechanical examples) it is shown in the papers https://arxiv.org/pdf/physics/0506203.pdf https://arxiv.org/pdf/1302.1212....
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1answer
123 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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88 views

Unitarity Gauge : how to undo the gauge transformation

I will simplify the argument. Let's consider a Gauge Boson (like the gauged one of U(1), $A_\mu$). Then, consider the Higgs boson with exponential representation, then $$H = e^{i\pi(x)/v}\left(\begin{...
2
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43 views

Gauge Permitting c Magnetic Vector and Instant Electric Scalar Potentials?

The Lorenz gauge requires c propagation of both scalar and vector potentials. The Coulomb gauge requires instant "propagation" of these potentials but is stated in such a way as to permit c ...
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175 views

Vector potential and gauge in electromagnetism

In a paper by Zimmerman [JOURNAL OF APPLIED PHYSICS 114, 044907 (2013)], it is stated that the Lorenz gauge in electromagnetism is the only gauge with real physical meaning. How do I reconcile this ...
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58 views

Gauge transformation issues of Proca Lagrangian

It seems to be trivial to claim that the mass term in Proca Lagrangian is NOT "gauge invariant". The claim show up in Wikipedia or section 6.3 in Greiner's book "Field Quantization". But I'm puzzled ...
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50 views

Is comoving coordinate a gauge choice?

Consider the Roberston Walker metric in 4D, $$ds^2 = -dt^2 + a^2(t) \left( \frac{dr^2}{1-kr^2} +r^2 d\Omega^2_2 \right)$$ Now, if we consider the collapse of a spherically symmetric fluid, spherically ...
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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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29 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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57 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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1answer
78 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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35 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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70 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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128 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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32 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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44 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
54 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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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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33 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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22 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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46 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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36 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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49 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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0answers
104 views

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
62 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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172 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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0answers
136 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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126 views

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
274 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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0answers
287 views

Coulomb Gauge under Lorentz Boost

In the Coulomb gauge for the Maxwell potential we have $$ A^0 = 0 \\ \partial_i A^i = 0 $$ Under an infinitesimal Lorentz Transformation with parameter $\epsilon$, we have $$ A^\mu(x) \rightarrow ...
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142 views

Gauged supergravity

It is said that in N=2 supergravity coupled to vector multiplets and hypermultiplets, one can gauge the R-symmetry by equivalently gauging the isometries of the corresponding hyperkahler cone over the ...
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54 views

Vertex of gauge boson interaction in an arbitrary gauge

Let's have interaction between some gauge boson (for example, $W$ boson) and some other field, for example, let assume $\bar{u}\gamma_{\mu}(1 - \gamma_{5})d W^{\mu} + h.c.$. Let's then use gauge $R_{\...
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0answers
733 views

Hamiltonian for Electron in Magnetic Field with Symmetric Gauge in Polar Coordinates

I am new on the board and have a question about how to write the Hamiltonian for an electron in a magnetic field rotating at a fixed radius. I would like to write the hamiltonian using the symmetric ...
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153 views

$E$ and $B$ fields in Axial Gauge

I am trying to compute the $\vec{E}$ and $\vec{B}$ fields in the Axial gauge ($n \cdot \vec{A}=0$) where $n^2=1$, but I'm having trouble seeing the usefulness/how it simplifies the equations.
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246 views

Is the axial gauge with a $\xi$ term useful in Yang-Mills theory?

i) Do people use axial gauge with a $\xi$ term? When $\xi\neq 0$, ghosts do not decouple, but maybe it's still useful? ii) Is it proved that the term $\frac 1 {2\xi}(n.A)^2$ in the Lagrangian does ...
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29 views

Is Lagrange multiplier an arbitrary gauge?

A related post might be found here: Is the gauge transform field in electromagnetism a Lagrange multiplier? Consider the case of Lagrange multiplier $L=f(x)+\lambda g(x)$ where $g(x)=0$ was a ...