10 votes
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What's the importance of all four fundamental forces being "curvature"?

When we study non-gravitational fundamental interactions, we distinguish internal symmetries associated with only such interactions from the external symmetries of spacetime. For all fundamental ...
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  • 22.5k
10 votes

Is gauge covariant derivative an ordinary covariant derivative?

The gauge covariant derivative is a genuine covariant derivative in the ordinary sense of differential geometry, but in the general sense of a (principal) connection form $A$ inducing covariant ...
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  • 109k
9 votes
Accepted

Does Coulomb gauge imply constant density?

You secretly impose 2 gauge fixing conditions: $$\nabla \cdot \vec{A} = 0$$ $$\nabla \cdot \vec{A} + \mu_0 \epsilon_0\frac{\partial \varphi}{\partial t} = 0$$ The latter coming from that fact you use ...
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  • 5,250
6 votes

BRST Symmetry and Single Particle States

It isn't obvious from that transformation alone. Remember that in P&S, the forward and backward polarization vectors are defined as: \begin{equation} \epsilon ^{\pm}_{\mu} = \frac{1}{\sqrt{2} |\...
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  • 1,098
5 votes

Is gauge covariant derivative an ordinary covariant derivative?

Whether space-time symmetries (as in GR) or internal symmetries (as in Yang-Mills) are gauged, covariant derivatives are defined such that $D_\mu U(g) X = U(g) D_\mu X$. To get a feel for this, I ...
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  • 5,194
5 votes
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BRST Symmetry and Single Particle States

I will post an answer because I have understood things in a certain way and I would like to share it. In this way, if it is wrong, I will get to know why it is wrong (if someone is kind enough to ...
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  • 2,119
4 votes

What is the asymptotic charge for a two-form theory in Lorenz gauge?

Covariant Phase Space Prescription The most straightforward way to compute the surface charge associated to an asymptotic symmetry is the covariant phase space prescription which I will outline in ...
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  • 30.2k
2 votes

Conservation of gauge charge

For $SU(N)$, the non-abeliean current density $j_\mu^a$ has $N^2-1$ components (ignoring the spacetime index), the same as the number of generators of the gauge group (which in turn are associated ...
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  • 35.5k
2 votes
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How do you multiply a 4x1 spinor by a $SU(3)$ matrix?

Color and Dirac/spinor indices are different types of indices. E.g. the quark field carries both.
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  • 172k
1 vote
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What would happen if you reduced the coupling of $SU(2)$ in the standard model to zero?

It is straightforward to see, even though your ultimate vision should be in trouble. I assume you mean decrease the coupling g of just SU(2), and leave the EM coupling e and the Higgs v.e.v. v alone, ...
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1 vote

What's the importance of all four fundamental forces being "curvature"?

In the 1920s–1940s, people developed a unified classical theory of gravity and electromagnetism using just this sort of approach. It's called Kaluza-Klein theory. Some aspects of it even generalize to ...
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