Maxwell action
= Maxwell action
{c}
{title2=$S_E=\tfrac14\int F_{\mu\nu}F_{\mu\nu}\,d^4x$}
The source-free <Maxwell Lagrangian> gives $S=-\tfrac14\int F_{\mu\nu}F^{\mu\nu}\,d^4x$ in mostly-minus Lorentzian signature. Its <Euclidean action> is the displayed positive quadratic functional of the <electromagnetic field tensor>. Variation, with boundary terms vanishing, yields $\partial_\mu F_{\mu\nu}=0$.