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7
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3answers
154 views

What role does “spontaneously symmetry breaking” played in the “Higgs Mechanism”?

In talking about Higgs mechanism, the first part is always some introduction to the concept of spontaneously symmetry breaking (SSB), some people saying that Higgs mechanism is the results of SSB of ...
2
votes
1answer
52 views

Does a Static E-field Increase the Gauge Invariant Vector Potential Without Bound?

The gauge invariant formulation of Maxwell's Laws (7.13): Indicates that the transverse electric field is the time derivative of the transverse vector potential. This gauge invariant vector ...
2
votes
1answer
236 views

Does the low-energy gauge structure depend on the choice of $SU(2)$ gauge freedom?

The starting point and notations used here are presented in Two puzzles on the Projective Symmetry Group(PSG)?. As we know, Invariant Gauge Group(IGG) is a normal subgroup of Projective Symmetry ...
1
vote
1answer
162 views

Free Electromagnetic field in Lorenz gauge

To get rid of the extra term in the QED Lagrangian we need to redefine the electromagnetic four-vector: $A^{\mu} \rightarrow A^{\mu} - \frac{1}{c} \partial_{\mu} a(x)$ where $a(x)$ is the function ...
0
votes
1answer
35 views

Higgs mass and EW precision tests

I'm trying to understand how the Higgs mass can influence EW precision tests. In order to do that I'm using the following document (section 4.3): http://arxiv.org/pdf/0706.0684v1.pdf There are a ...
9
votes
0answers
302 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 ...
8
votes
0answers
227 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
137 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. ...
6
votes
0answers
317 views

gauge invariance of the Feynman amplitudes

When we calculate the photon polarization sums over amplitudes, $$X=\sum\limits_{r=1}^{2}|\mathcal M_r|^2=\mathcal M_\alpha\mathcal M_\beta^*\sum\limits_{r=1}^{2}\epsilon_r^\alpha\epsilon_r^\beta$$ ...
4
votes
0answers
183 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
votes
0answers
188 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
votes
0answers
170 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
66 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
65 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 ...
3
votes
0answers
131 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
290 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
191 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
39 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 $W_{\mu}^{1,2,3}$ ...
2
votes
0answers
57 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
99 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
132 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 ...
2
votes
0answers
36 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
60 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
68 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 ...
2
votes
0answers
44 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
84 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 ...
1
vote
0answers
29 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
44 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
71 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
114 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
165 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
22 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 ...
0
votes
0answers
41 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 ...
0
votes
0answers
28 views

global transformations in 3d gravity

I am currently working on proper and improper gauge transformations in 3d gravity and btz black holes. (because I have seen it defined with many different ways I will just say that with "proper"and ...
0
votes
0answers
43 views

Gauge invariance of classical XY spin model

I am trying to understand gauge invariance as it is applied to a XY model Any ideas if it is in fact gauge invariant? Examples of how it is or isn't would be very helpful. If it is not gauge ...
0
votes
0answers
37 views

Does fixing a metric component have anything to do with diffeomorphism invariance?

It is well known that in general relativity, the metrics $g_{\mu \nu}$ and $g_{\mu \nu} + \epsilon L_\xi g_{\mu \nu}$ are physically equivalent, where $L_\xi g_{\mu \nu}$ is the Lie derivative of the ...
0
votes
0answers
40 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 ...
0
votes
0answers
95 views

What is wrong in following arguments about connection of local gauge invariance and causality?

There is a question and corresponding downvoting of my answer, so I decided to ask this question. There is my answer on it: "...The most theories of free fields are invariant under global gauge ...
0
votes
0answers
61 views

Physical and dynamical components the four potential

I have a question regarding the four-potential and its gauge symmetry. We have a gauge freedom: $A_{\mu} \rightarrow A_{\mu} + \partial_{\mu}\chi$ Such a transformation does not alter the EM field. ...
0
votes
0answers
92 views

How to charge a field?

In a previous post [ Noether theorem, gauge symmetry and conservation of charge ] we were discussing the different ways to demonstrate the current conservation: via the first Noether theorem applied ...