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4
votes
2answers
367 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 ...
13
votes
4answers
749 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 ...
7
votes
2answers
595 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 ...
3
votes
1answer
281 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 ...
2
votes
0answers
106 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 ...
1
vote
2answers
229 views

Gauge theory in classical electromagnetism

I understand gauge theory as the theory of continuous transformation group which keeps Lagrangian (or dynamics) invariant. So some integral invariants could be found. In terms of classical ...
3
votes
1answer
357 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?
4
votes
3answers
270 views

Problems with putting mass on Yang-Mills theory by hand

When Yang-Mills field theory was introduced, a problem is that the gauge invariance can not allow mass for the gauge field. Later people invented spontaneous symmetry breaking and Higgs mechanism to ...
4
votes
3answers
249 views

Why gauge theories have such a success?

[This question was inspired by a identical question asked on a other forum] Note that we may morally include general relativity in the gauge theories. We may have several (some are deliberately ...
4
votes
2answers
360 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 ...
4
votes
1answer
495 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, ...
5
votes
1answer
239 views

6 independent Einstein field equations?

I can't understand the comment on page 409, Gravitation, by Misner, Thorne, Wheeler It follows that the ten components $G_{\alpha\beta} =8\pi T_{\alpha\beta}$ of the field equation must not ...
4
votes
2answers
313 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 ...
3
votes
1answer
258 views

How to introduce the electromagnetic field in Quantum Field Theory?

There are many ways to introduce the electromagnrtic field in Quantum Field Theory(QFT), such as canonical quantization method which introduces the creation and annihilation oprators by treating the ...
1
vote
1answer
231 views

Local gauge invariance and fields

I have one question about local gauge invariance of the spinor and scalar theories. For the scalar complex field with lagrangian $L_{0}$ requirement of local gauge invariance leads us to the ...
1
vote
2answers
271 views

A simple question on $SU(2)$ gauge transformations in Wen's papers on projective symmetry group (PSG)?

Recently I am studying the projective symmetry group (PSG) and the associated concept of quantum order first proposed by prof.Wen. In Wen's paper, see the last line of Eq.(8), the local SU(2) gauge ...
4
votes
2answers
196 views

Local guage symmety implies causality

I read in a QFT book that local gauge symmetry implies causality. Could someone please explain that statement and why it's true? Thank you.
3
votes
1answer
90 views

What are type system examples of local gauge transformation- and field strength-like objects?

This is essentially a follow up motivated by this answer to my question about the gauge transformation interpretation of identity types. A field $$\psi:\mathcal M\to\mathbb C^n$$ is a section of the ...
3
votes
0answers
206 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 + ...