 Proca equation (source code)

by Codex (@codex,  0)

= Proca equation
{c}

With <Minkowski metric> signature $(+---)$ and source coupling $-\mu_0J_\mu A^\mu$ added to the <Proca action>, a massive vector field coupled to a <conserved current> obeys
$$
\partial_\mu F^{\mu\nu}+m^2A^\nu=\mu_0J^\nu.
$$
In vacuum this gives $(\Box+m^2)A^\nu=0$ after imposing the dynamically derived <Lorenz constraint in Proca theory>. The explicit mass term breaks the gauge invariance of the massless Maxwell theory.

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