Invariance of a physical system (its action) under a continuous group of local transformations underlain by a global symmetry whose group parameters fixed in space-time have now been extended to vary in space-time instead. Use for buildup of the invariance, fixing the gauge, and accounting for the ...

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13
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305 views

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 ...
10
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0answers
313 views

Gauge invariant but not gauge covariant regularization

I'm not sure if someone's already asked this before, but I was wondering, in field theory, when we say that a certain field is gauge invariant but not gauge covariant, what does this mean? In ...
9
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0answers
218 views

Faddeev Popov Gauge Fixing in Electromagnetism

Reading section 9.4 in Peskin, I am wondering about the following: The functional integral on $A_{\mu}$ diverges for pure-gauge configurations, because for those configurations, the action is zero. ...
9
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0answers
320 views

Gauge fields in Polyakov's treatment of renormalization for nonlinear sigma model

I am deriving the results of renormalization for nonlinear sigma model using Polyakov approach. I am closely following chapter 2 of Polyakov's book--- ``Gauge fields and strings''. Action for the ...
6
votes
0answers
518 views

gauge invariance of the Feynman amplitudes

When we calculate the photon polarization sums over amplitudes, $$X=\sum\limits_{r=1}^{2}|\mathcal M_r|^2=\mathcal M_\alpha\mathcal M_\beta^*\sum\limits_{r=1}^{2}\epsilon_r^\alpha\epsilon_r^\beta$$ ...
5
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0answers
43 views

In a perturbative FRW cosmology, why do constant-density hypersurfaces define a good gauge?

It appears to be common in the discussion of perturbative FRW cosmologies to choose a gauge using hypersurfaces for special values of some quantity, like surfaces of constant density $\rho$, constant ...
4
votes
0answers
374 views

Gauge Invariance of Yang Mills Lagrangian

I am trying to show the invariance of the following Yang Mills Lagrangian: $$L= -\frac{1}{4} F^a_{\mu \nu} F_a^{\mu\nu} + J_a^\mu A_\mu^a$$ under the following gauge transformation ($\theta$ being a ...
4
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0answers
470 views

Gauge Invariance of the Non-abelian Chern-Simons Term

I'm trying to prove that, under the gauge transformation $$A_{\mu} \rightarrow A_{\mu}^{\prime} = g^{-1} A_{\mu} g + g^{-1} \partial_{\mu} g,$$ the non-abelian Chern-Simons Lagrangian density: $$\...
4
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0answers
185 views

Wilson lines, boundary conditions, surface defects of TQFTs

I asked the following question in mathematics stack exchange but I'd like to have answers from physicists too; I have been studying (extended) topological quantum field theories (in short TQFTs) from ...
3
votes
0answers
41 views

Energy Spectrum and Gauge Transformations

There is a question in SE about the fact that the Hamiltonian isn't invariant under the EM gauge transformations. I wanted to ask about its consequences here. I know that in general, the Hamiltonian ...
3
votes
0answers
48 views

Number of Independent postulates in Electrodynamics

We know that there are two ways to get charge conservation in electrodynamics by using the following action: $$S[A]~=~\int\! d^4x {\cal L},$$ $$ {\cal L} ~=~{\cal L}_{\rm Maxwell} + {\cal L}_{\rm ...
3
votes
0answers
113 views

Classical electrodynamics as an $\mathrm{U}(1)$ gauge theory

Preface: I haven't studied QED or any other QFT formally, only by occasionally flipping through books, and having a working knowledge of the mathematics of gauge theories (principal bundles, etc.). ...
3
votes
0answers
82 views

Why are gauge symmetries continuous?

All gauge theories that are considered in literature are continuous $SU(N)$ symmetric. My question is why are always continuous groups considered for gauge symmetries? Why don't we consider discrete ...
3
votes
0answers
86 views

Gauge invariance of Fermi's golden rule

I am having some issues with gauge invariance of Fermi's golden rule. Say we have a system Hamiltonian for a particle in an electric field and some additional potential $V$ with \begin{equation}H=(p-A(...
3
votes
0answers
157 views

Symmetry, gauge, and projective symmetry group (PSG)?

My following questions come from the understanding of the relations between the PSGs for two gauge-equivalent mean-field (MF) Hamiltonians (or MF ansatz). Considering the Schwinger-fermion ($f_{\sigma}...
3
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0answers
102 views

The Ward identity for EM amplitude with massive vector boson

Let's have theory of massive vector boson interacting with EM field: $$ L = |D_{\mu}W_{\nu} - D_{\nu}W_{\mu}|^{2} + m^{2}|W|^{2}, \quad D_{\mu} = \partial_{\mu} - ieA_{\mu}. $$ The question: how to ...
3
votes
0answers
139 views

Is the $SU(2)$ flux defined in the context of Projective Symmetry Group(PSG) an observable quantity?

The $SU(2)$ flux defined in the context of PSG is as follows: Consider the mean-field Hamiltonian $H_{MF}=\sum(\psi_i^\dagger\chi_{ij}\psi_j+H.c.)$ description of a 2D lattice spin-model, the ...
3
votes
0answers
344 views

Gauge invariance of gg->gg scattering amplitude?

I'm trying to calculate the spin and color averaged gg->gg cross section, and I am stumbling upon gauge invariance: Must the amplitude not be invariant under replacements $\epsilon_i \to \epsilon_i + ...
3
votes
0answers
196 views

Attempts to explain Higgs coupling as a gauge transformation symmetry

As is (supposedly) well known, Electromagnetic coupling can be "explained" as a closure term to a langrangian comprising a free Dirac field and a free vector field that are required to be invariant ...
2
votes
0answers
53 views

Physical proceses before the breaking of $SU(2)_L\times U(1)_Y$ symmetry

The energy scale which the electromagnetic and the weak interaction were unified, there were 4 massless gauge bosons: 3 corresponding to the unbroken generators of $SU(2)_L$, say $W_{\mu}^{1,2,3}$ and ...
2
votes
0answers
83 views

(Super)Gauge Fixing in Supersymmetry

I have three questions about gauge fixing in supersymmetry, one is general and the other two explicit: Why gauge fixing seems not important in supersymmetry? By "not important" I mean gauge fixing ...
2
votes
0answers
178 views

Is global gauge symmetry really a symmetry and local conserved current in gauge theories?

One way to define a gauge theory is that whenever the Lagrangian is invariant under some local transformations, we say these local transformations are local gauge transformations and the theory is a ...
2
votes
0answers
58 views

Massive photon and gauge invariance of S-matrix amplitude

Let's have minimally extended gauge invariant lagrangian (with free kinetic term of EM field): $$ \tag 1 L (\Psi , \partial_{\mu} \Psi) \to L (\Psi , D_{\mu}\Psi ) - \frac{1}{4}F^{\mu \nu}F_{\mu \nu}, ...
2
votes
0answers
68 views

Momentum operator of a particle in an electromagnetic field

In quantum mechanics, to all observables correspond some self-adjoint operators. In the absence of an electromagnetic field the momentum operator is clearly $\vec{P}:=\frac{\hbar}{i}\vec{\nabla}$. ...
2
votes
0answers
49 views

What's the necessary and sufficient condition for gauge equivalence in the projective construction?

The definition of gauge equivalence and notations used here is the same as those in my previous question. As we know, the condition $\chi_{ij}'=G_i\chi_{ij}G_j^\dagger$(where $G_i\in SU(2)$) is a ...
2
votes
0answers
87 views

CP-symmetry and Ward identities and finite temperature

I have a few questions about Ward-identities which I summarize here. For each I am very greateful for answers and references to literature. Wikipedia states about Ward-identities: The Ward-...
1
vote
0answers
25 views

Gauge invariance of non-Abelian theories under Pauli-Villars-Regularisation

Under the ordinary Pauli -Villars Regularisation one introduces a heavy mass ($\Lambda$) term $$\frac{1}{p^2-m^2+i\epsilon} \rightarrow \frac{1}{p^2-m^2+i\epsilon} - \frac{1}{p^2-\Lambda^2+i\epsilon}....
1
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0answers
21 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{...
1
vote
0answers
44 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 ...
1
vote
0answers
50 views

Gauge invariance in gravitational field

I have read that the linearized equation for the metric fluctuations $h_{\mu\nu}$, namely: $$ \partial^2h^{\mu\nu}-\partial_{\alpha}(\partial^{\mu}h^{\nu\alpha}+\partial^{\nu}h^{\mu\alpha}) +\partial^...
1
vote
0answers
24 views

Photo's vector characteristic

In Frank Close's infinity puzzle, it says that to maintain the invariance for electric charge requires some means to transmit information about the local charge of gauge to electric charges elsewhere. ...
1
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0answers
104 views

Derivation of Schrodinger equation using unitary operators

I encountered the derivation of Schrodinger time dependent equation using expansion of a unitary time propagation operator into power series in a small quantity $\delta t$, working to first order in $\...
1
vote
0answers
48 views

Noether Charge and Gauge Fields

I understand the global gauge symmetry results conserved charges associated with the symmetry. My question is, why don't we have conserved charges associated with local gauge symmetry of the gauge ...
1
vote
0answers
63 views

Noether's 2nd Theorem and Local Gauge Identities

I am trying to derive the so called Gauge Identities: \begin{equation} D_\nu\frac{\delta S}{\delta\phi} = 0 \end{equation} Where $D_\nu$ is an operator involving derivatives and $\frac{\delta S}{\...
1
vote
0answers
71 views

Are hilbert spaces invariant under gauge transformations?

I'm trying to work out if the physical hilbert space is invariant under any gauge transformation? I have found situations where under some transformations they don't change but I've now gotten very ...
1
vote
0answers
118 views

Is gauge invariance essential to a theory be renormalizable?

Let's consider a model of New Physics in which all operator have dimension smaller than four, but which breaks explicitly $SU(2)_L$ gauge symmetry. Is this model necessarily renormalizable? ...
1
vote
0answers
96 views

Argument of E. Fradkin on the mean-field theory of spin liquids

I have read the chapter 8 of Field Theory of Condensed Matter Physics (2ed.) by E. Fradkin a couple of times, but I still confused by his argument at some points. I hope you can help me with that. ...
1
vote
0answers
55 views

Gauge invariance and non-commuting second derivatives

I'm currently doing a homework assignment in relativistic quantum mechanics, and one of the problems involves proving the gauge invariance of a particular lagrangian. The problem is really quite ...
1
vote
0answers
132 views

How can gauge invariance be unphysical?

Gauge symmetry is said to be "unphysical" because the transformations - unlike changes of reference frame - do not correspond to real physical operations. But the consequences of gauge symmetries are ...
1
vote
0answers
187 views

Yang-Mills Coulomb Gauge

My Question is how to explicitly move into the "Coulomb gauge" in Yang-Mills theory. Using the answer provided by QMechanic, one can move into the "temporal gauge" for Yang-Mills fields: Gauge fixing ...
0
votes
0answers
38 views

Is my proof of Proca Lagrangian local gauge invariance correct?

My task was to prove that the first term of the Proca Lagrangian is invariant under local gauge transformations. I’m new to Ricci calculus and think I’ve misinterpreted what I was supposed to do, and ...
0
votes
0answers
49 views

From gauge invariance to charge conservation in covariant electrodynamics

I tried to solve the equations of motion using the action for the electromagnetic field interacting with a current, like $$ L = F_{\mu\nu}F^{\mu\nu} + A_{\nu}j^{\nu} $$ getting the right Maxwell's ...
0
votes
0answers
23 views

Laplacian equations and transformation invariance and homogeneous functions

Functions whose Laplacian is zero are said to be harmonic. 1) Do harmonic functions always imply a conservation law and transformation invariance of some kind? 2) Homogeneous functions do not admit ...
0
votes
0answers
55 views

What is the difference between length and velocity gauge when it comes to a dipole approximation?

Lets say we have plane wave with $\vec E$ perpendicular to $\vec k$. The dipole term will come from $\vec A\cdot \vec p$. Is the electric field longitudinal in the length gauge for the dipole ...
0
votes
0answers
37 views

Gauge invariance of quantum scalar field coupled to classical electromagnetic potential

I would like to quantize a scalar field that is coupled to a classical electromagnetic field $A_\mu$. More precisely, I start with the action (signature -+++) $$ S=\int d^4x\left(-|(\partial_\mu+iqA_\...
0
votes
0answers
55 views

Different Signs in Yang Mills Gauge Transformations

I have seen the Yang-Mills Gauge Theory be constructed in many books and papers, however I have seen pretty much equal disparage of + and minus signs in the following equations, the definition of the ...
0
votes
0answers
44 views

Expansion of comparator

Currently I am working on Pesking Schroeder Section 15.1 and trying to understand the expansion given in (15.5), which is $$ U(x+\epsilon n, x) = 1 - i\,e\,\epsilon\,n^{\mu}\,A_{\mu}(x)+O(\epsilon^2) $...
0
votes
0answers
19 views

When considering local phase transformations are we forced to use covariant derivatives?

When considering local phase transformations $e^{i\theta(x)}$ of the fields $\phi$ and $\phi^*$ corresponding to \begin{equation} \mathcal{L}=\partial_\mu\phi^*\partial^\mu\phi-m^2\phi^*\phi \end{...
0
votes
0answers
39 views

Galileons and the brane origins of their Galilean invariance

I've been reading through a paper on Galileons by K. Hinterbichler et al. in which they discuss the brane origin of their Galilean invariance (starting on page 9) http://arxiv.org/abs/1008.1305 The ...
0
votes
0answers
69 views

About equivalence of two ways of “derivation” of Standard model

Two ways of SM derivation I know two methods of SM lagrangian "derivation". The first one, which I will call as Weinberg way, is based on approaches of SM as theory with spontaneusly broken $SU(2)_{...