3
votes
2answers
83 views

Utility of gauge four-potential $A_{\mu}$ (as opposed to electric and magnetic fields ${\bf E}$ and ${\bf B}$) in E&M?

The action for an electromagnetic field with source charges is given by $$S= \int \left\{ \frac{1}{4\mu_0}F^{\mu\nu}F_{\mu\nu} - J^\mu A_\mu \right\}dx$$ By setting $dS=0$ and taking the Lorenz ...
8
votes
2answers
127 views

Counting the number of propagating degrees of freedom in Lorenz Gauge Electrodynamics

How do I definitively show that there are only two propagating degrees of freedom in the Lorenz Gauge $\partial_\mu A^\mu=0$ in classical electrodynamics. I need an clear argument that involves the ...
0
votes
0answers
58 views

Explanation of the classical coupling of the Higgs Field to Electromagnetism

I'm interested in learning about the classical coupling of the Higgs Field to Electromagnetism. There are numerous sources explaining the Higgs mechanism quantum mechanically, i.e. How does the Higgs ...
7
votes
4answers
398 views

Why does electric field intensity $E$ can be uniquely determined by its divergence and curl? [duplicate]

My question is, the number of following equations $$\nabla\cdot E=\frac{\rho}{\varepsilon}$$ $$\nabla\times E=-\frac{\partial B}{\partial t}$$ is 4 while the number of unknown variables ...
13
votes
4answers
744 views

Can we measure an electromagnetic field?

As far as I can check, the Aharonov-Bohm effect is not -- contrary to what is claimed in the historical paper -- a demonstration that the vector potential $A$ has an intrinsic existence in quantum ...
16
votes
2answers
391 views

Coulomb gauge fixing and “normalizability”

The Setup Let Greek indices be summed over $0,1,\dots, d$ and Latin indices over $1,2,\dots, d$. Consider a vector potential $A_\mu$ on $\mathbb R^{d,1}$ defined to gauge transform as $$ A_\mu\to ...