# Questions tagged [gauge-invariance]

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 corresponding changes in the functional measure of the system.

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### Gauge Invariance in Quantum Mechanics for Charged Particle

In Sakurai's book chapter 2, he has discussed the diffence between canonical momentum and kenitic momentum under gauge transformatiom. The former should be gauge-dependent, and the latter one would be ...
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### Why are physical states not eigenstates of BRST charge?

In many texts in quantum field theory or string theory, it is stated that the BRST charge $Q$ must annihilate physical states because the states are required to be BRST invariant. Since $Q$ generates ...
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### Trouble reconciling these two views on gauge theory

Very generally speaking, I view gauge theory as asking what local symmetries leave our theory invariant and then seeing the consequences. Thus, taking a look at the Lagrangian for electromagnetism, we ...
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### Gauge invariance in QED with just fermion transformations

I've got myself confused about a basic question. If we have a gauge-invariant operator $\mathcal{O}$ whose expectation value is \left\langle\mathcal{O}\left(x_1, \ldots, x_n\right)\...
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### Canonical and kinetic momenta vs gauge dependence

I am struggling a bit to understand the concept of gauge invariance/dependence with canonical momentum. For instance, if we consider a Hamiltonian of a particle in an electromagnetic field described ...
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### Stueckelberg mechanism for interacting QFTs

The Stueckelberg mechanism or "trick" (see e.g. Section 4 of https://arxiv.org/abs/1105.3735) is basically a method to take the massless limit of massive gauge theories in a smooth way, ...
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### Why can't we gauge the Lorentz group? (Or can we?)

One of the (many different, somewhat independent) routes to gauge theory is to start from a global symmetry of some kind and "gauge" it, which involves promoting it to a local symmetry and ...
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### Gauge transformation with complex parameter in quantum mechanics with minimal substitution

This follows from the question Can an Electromagnetic Gauge Transformation be Imaginary? It's about the Hamiltonian $$H=\frac{(p-A)^2}{2m}$$ in units where $c=e=\hbar=1$. The question regarded a gauge ...
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### Are all actions time reparameterization invariant?

Let's concentrate on point particle mechanics on a one dimensional manifold for simplicity. The action is $$S [q,\dot{q}]=\int dt L(q,\dot{q},t).$$ Time reparameterization would involve $t \to t'=f(t)$...
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### How is related the exponential map, the covariant derivative and the gauge transformations under Lie groups

I will try to formulate my question the best way possible considering my lack of mathematical formalism. I just want to know, in every aspects, why spinors transforms (under Lorentz transformations) ...
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### Flavor changing neutral current with photon

I'm trying to understand why the penguin diagram for photons takes its form. $I$ here is the integral and some CKM elements. The author (Ch1.6.1) says that for $b\rightarrow s\gamma$, we get a factor ...
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### Original motivation for promoting global symmetries to local

Assume we are dealing with a Lagrangian $\mathcal{L}$ for matter field $\psi$ which has a global $G$-symmetry and it's possible to promote this global $G$-symmetry to a local symmetry after the usual ...
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### Non-diagonal matrix element in the Wannier functions basis

I'm going through Marzari's paper about maximally localized wannier functions. There is a passage I'm trying to understand but can't seem to get. On the third page, between equation 5 and 6, they have ...
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### Differential Forms and Gauge Invariance?

In the Sean Carroll book on GR, page 86 in chapter 2 says $$d(A+d\lambda)=F,$$ where $A$ is vector potential and $\lambda$ is some $0$-form scalar. $F$ is the electromagnetic field strength tensor. I ...
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### Gauge-fixing condition invariant under auxiliary gauge transformation

In quantum gravity one usually splits the metric $g= \bar{g}+h$ into a background field $\bar{g}$ and a fluctuation field $h$. In order to obtain a propagator one has to gauge fix the action (e.g. ...
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### Section 80 of Dirac's book: Principles of Quantum mechanics

I am looking for informations about one of Dirac's calculation: in his book Principles of Quantum Mechanics (4th edition), he developed inside section 80 a gauge-invariant version of QED in which he ...
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### Invariance of gauge-fixing condition in background field method

In the Peskin & Schröder (chapter 16.6) they use the background field method and spilt the gauge field into an background field $A$ and a fluctuation field $\mathcal{A}$. Next they claim that the ...
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### Faddeev-Popov trick in QED Peskin and Schroeder

On page 297 of Peskin and Schroeder, the book obtains the propogator $$\tag{9.58} \tilde{D}_F^{\mu\nu}(k)=\frac{-i}{k^2+i\epsilon}\bigg(g^{\mu\nu}-(1-\xi)\frac{k^\mu k^\nu}{k^2}\bigg).$$ The book then ...
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### Symmetry breaking, gauge invariance and superconductivity

I still have some confusions over symmetry breaking in superconductivity. To begin with it’s clear gauge symmetry can’t be spontaneously broken, since it’s not a symmetry to begin with. I want to ...
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### Residual gauge freedom and complete residual gauge fixing in lorenz gauge

What I understand after reading all answers from physics stack exchange related to residual gauge freedom and complete residual gauge fixing are as follows; The gauge transformation is: $A'_{\mu}$=\$A_{...