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4 votes
Accepted

What makes electric and magnetic fields in Yang-Mills theories gauge co-variant?

In YM theory, the field strength $G$ is not invariant under gauge transformations. Indeed, under the gauge transformation $$ A_{\mu} \to \Omega(x) A_{\mu} \Omega^{-1}(x) + i \Omega(x) \partial_{\mu} \...
Gabriel Ybarra Marcaida's user avatar
2 votes
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Is the bundle of the Aharonov-Bohm effect like the tangent bundle of a cylinder or like the tangent bundle of a truncated cone?

Requiring (the derivative of) the wavefunction to be horizontal w.r.t. the $U(1)$-connection is absurd. If you just consider a free particle in space moving in the absence of any field at all (so ...
HTNW's user avatar
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2 votes
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Effect of gauge-fixing via Lagrange multipliers on Euler-Lagrange equations

OP has correctly identified the mechanism in their example: In order for OP's action (4) to be gauge invariant, we must assume the continuity equation (3). Eq. (3) in turn implies that the Lagrange ...
Qmechanic's user avatar
  • 204k
1 vote
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Visualization of a gauge field with non-null winding number

The proper answer is that fully visualizing this winding would involve imagining the winding on a 3-sphere. Just in case someone reading this doesn't know why that is, it's because the boundary ...
11zaq's user avatar
  • 428
1 vote
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Abelian Chern-Simons large gauge transform

Yes. This rely on the fact that $\eta$ (which may be a multiple-valued closed 1-form) and $F=\mathrm{d}A$ (which may be a non-exact closed 2-form) are both assumed to have integral periods. Then the ...
Qmechanic's user avatar
  • 204k
1 vote
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Meaning of “transforms like the adjoint” in the context of Yang Mills Theory and connection to Lie Algebra

I'm not sure which subquestions are still obscure. Using a,b,... for the $N^2-1$ adjoint indices and i,j,... for the fundamental ones, and summation over repeated indices, you have $$ F^a \qquad \...
Cosmas Zachos's user avatar
1 vote

Meaning of “transforms like the adjoint” in the context of Yang Mills Theory and connection to Lie Algebra

"The adjoint representation" of a Lie group $G$ is in the end only a name for the Lie algebra $\mathfrak{g}$ of that group. The $W\mapsto UWU^\dagger$ transformation rule comes from the ...
ACuriousMind's user avatar
  • 126k
1 vote
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Can we impose Coulomb gauge without using temporal gauge in source-free Maxwell electrodynamics?

It is true that in your case there is no visible difference between the Coulomb gauge and the $\phi=0$ (Weyl) gauge. But this is because you didn't include a source! If you do include it, so $\vec{E} =...
Gabriel Ybarra Marcaida's user avatar

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