The gauge-invariance tag has no wiki summary.
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Are waves on water an example of gauge invariance?
So: Is the close similarity of small waves crossing water of varying depths ("depth potentials") an example of an approximate gauge invariance?
If so, do other "only the surface dynamics matter" ...
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0answers
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The gauge-invariance of the probability current
It is simple to show that under the gauge transformation $$\begin{cases}\vec A\to\vec A+\nabla\chi\\
\phi\to\phi-\frac{\partial \chi}{\partial t}\\
\psi\to \psi ...
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1answer
69 views
Invariance, covariance and symmetry
Though often heard, often read, often felt being overused, I wonder what are the precise definitions of invariance and covariance. Could you please give me an example from quantum field theory? ...
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377 views
When can a global symmetry be gauged?
Take a classical field theory described by a local Lagrangian depending on a set of fields and their derivatives. Suppose that the action possesses some global symmetry. What conditions have to be ...
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71 views
How to charge a field?
In a previous post [ Noether theorem, gauge symmetry and conservation of charge ] we were discussing the different ways to demonstrate the current conservation: via the first Noether theorem applied ...
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1answer
147 views
Local $U(1)$ gauge invariance of QED
The Lagrangian density for QED is
$$ \mathcal{L}=-\frac{1}{4}F^{\mu\nu}F_{\mu\nu}+\bar{\psi}(i\gamma^{\mu}D_{\mu}-m)\psi $$
with
$$F_{\mu\nu}=\partial_{\mu}A_{\nu}-\partial_{\nu}A_{\mu} $$
$$ ...
3
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1answer
134 views
What conservation law corresponds to this local $U(1)$ symmetry of the CCR?
It is known that canonical commutation relations do not fix the form of momentum operator. That means that if canonical commutation relations (CCR) are given by
...
4
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2answers
334 views
Is spacetime an illusion?
In consistent histories, for gauge theories, can the projection operators used in the chains be not gauge invariant?
In quantum gravity, for a projection operator to be gauge invariant means it has ...
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2answers
75 views
Charged quantum particle in a magnetic field - choosing a different gauge leads to different wavefunctions
Consider a charged quantum particle confined to the $xy$ plane, subject to a magnetic field $\mathbf{B}=B\hat{z}$.
The Hamiltonian is:
$$ H = \frac{1}{2m} \left( \mathbf{p} - \frac{e ...
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2answers
287 views
Vector Potential and Gauge Invariance in Quantum Mechanics
In classical electromagnetism, we are allowed to use gauge invariance through the argument that the only physical observable fields are the $E$-field and the $B$-field. So in that sense the scalar ...
2
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1answer
147 views
SU(3) gauge invariance in QCD
In QCD, the gauge-invariant lagrangian under the trasformation
$ \psi \to \psi' = e^{ig T^a \theta^a(x)} \psi$
is written as:
$\mathcal{L} = \bar{\psi}(i\gamma^\mu D_\mu - m)\psi - ...
3
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2answers
231 views
The physicality of the photon propagator
The equation for the photon propagator is straightforward
$$
D_{ij} = \langle 0 |T \{ A_{i}(x')A_{j}(x) \}|0 \rangle
$$
However, $A_{i}(x)$ is gauge-dependent and therefore unphysical (in the arguable ...
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0answers
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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 ...
2
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0answers
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What is non-Abelian about non-Abelian Chern-Simons' theory?
One is aware that in the axial gauge (say the light-cone gauge $A_{-}=0$) non-supersymmetric Chern-Simons' theory is a quadratic theory. Hence in this gauge there are no gauge-gauge interactions. Then ...
2
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2answers
165 views
Is the artificial gauge field a gauge field?
The so-called artificial gauge fields are actually the Berry connection. They could be $U(1)$ or $SU(N)$ which depends on the level degeneracy.
For simplicity, let's focus on $U(1)$ artificial gauge ...
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4answers
351 views
To which extent is general relativity a gauge theory?
In quantum mechanics, we know that a change of frame -- a gauge transform -- leaves the probability of an outcome measurement invariant (well, the square modulus of the wave-function, i.e. the ...
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2answers
205 views
Why is the “canonical momentum” for the Dirac equation not defined in terms of the “gauge covariant derivative”?
The canonical momentum is always used to add an EM field to the Schrödinger/Pauli/Dirac equations. Why does one not use the gauge covariant derivative? As far as I can see, the difference is a factor ...
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1answer
123 views
In a gauge theory, are two states related by a global phase transformation identified?
In a gauge theory (non-abelian for this question), I am told that two states $|\psi\rangle$ and $|\phi\rangle$ are to be identified if they are related by a gauge transformation $U(x)$
...
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1answer
130 views
Why Must Conserved Currents of Lorentz Symmetry Satisfy the Lorentz Algebra
I've seen it written many times that the commutation relation
$[M^{I-},M^{J-}]=0$
is required for Lorentz invariance in the light cone gauge quantisation of the bosonic string. This follows ...
3
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0answers
112 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 ...
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1answer
191 views
Large gauge transformations
I would like to understand what is the importance of large gauge transformations. I read that these gauge transformation cannot be deformed to the identity, but why should we care about that?
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2answers
271 views
Gauge fixing and equations of motion
Consider an action that is gauge invariant. Do we obtain the same information from the following:
Find the equations of motion, and then fix the gauge?
Fix the gauge in the action, and then find the ...
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2answers
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Cosmological relativistic effects : misunderstanding between cosmological and relativistic communities?
I would like to clarify something that mixes cosmology and relativistic effects. Maybe I'm not understanding something or maybe there a difference of vocabulary between the cosmological and the ...
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2answers
283 views
Intuition for gauge parallel transport (Wilson loops)
I'm looking for a geometrical interpretation of the statement that "Wilson loop is a gauge parallel transport".
I have seen QFT notes describe U(x,y) as "transporting the gauge transformation", and ...
5
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2answers
322 views
If gauge symmetries are fake, then why do we care if they are anomalous?
My understanding is that gauge symmetries are fake in that they are only redundancies of our description of the system that we put in (either knowingly or unknowingly) see Gauge symmetry is not a ...
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0answers
137 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 + ...
5
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3answers
490 views
Why can't gauge bosons have mass?
Clearly, a mass term for a vector field would render the Lagrangian not gauge-invariant, but what are the consequences of this? Gauge invariance is supposed to be crucial for the renormalisation of a ...
3
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1answer
327 views
Noether current for the Yang-mills-higgs lagrangian
I am trying to calculate the Noether's current, more specifically, the energy density of the Yang-mills-Higgs Lagrangian. Please refer to the equations in the Harvey lectures on Magnetic Monopoles, ...
6
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1answer
107 views
Request for Reference: BRST formalism/transformations
Could anyone please suggest a very basic paper/reference/literature on BRST symmetry/formalism that requires rudimentary knowledge of Dirac's method for dealing with constrained systems and generation ...
1
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1answer
201 views
Conserved quantum observables from symmetries *with density matrix*
I’ve read Ballentine where he derives the conserved observable operators (momentum, energy, ...) from symmetries of space-time.
Can I read up such a derivation in more detail somewhere else or even ...
4
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2answers
220 views
Can an Electromagnetic Gauge Transformation be Imaginary?
The Hamiltonian of a non-relativistic charged particle in a magnetic field is
$$\hat{H}~=~\frac{1}{2m} \left[\frac{\hbar}{i}\vec\nabla - \frac{q}{c}\vec A\right]^2$$.
Under a gauge transformation ...
3
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0answers
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Attempts to explain Higgs coupling as a gauge transformation symmetry
As is (supposedly) well known, Electromagnetic coupling can be "explained" as a closure term to a langrangian comprising a free Dirac field and a free vector field that are required to be invariant ...
3
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427 views
How does non-Abelian gauge symmetry imply the quantization of the corresponding charges?
I read an unjustified treatment in a book, saying that in QED charge an not quantized by the gauge symmetry principle (which totally clear for me: Q the generator of $U(1)$ can be anything in ...
5
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2answers
280 views
Gauge invariant Chern-Simons Lagrangian
I have to prove the (non abelian) gauge invariance of the following lagrangian (for a certain value of $\lambda$):
$$-\frac14 F^{\mu\nu}_aF_{\mu\nu}^a + ...
6
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1answer
48 views
“gauge fixed world-sheet action”
My question is in reference to the action in equation 4.130 of Becker, Becker and Schwartz.
It reads as,
$S_{matter}= \frac{1}{2\pi}\int (2\partial X^\mu \bar{\partial}X_\mu + \frac{1}{2}\psi^\mu ...
