On the $\Theta$-term in electrodynamics

Abstract

The term $\Theta\epsilon^{\mu\nu\rho\sigma}F_{\mu\nu}F_{\rho\sigma}$, when added to the electromagnetic Lagrangian $-{1\over 16\pi}F^{\mu\nu}F_{\mu\nu}$, does not change the signature of the Lagrangian. Actually, it increases the part with negative kinetic energy term at the spatial infinity. For this reason it does not change the conclusion, that at the spatial infinity the magnetic part of the electromagnetic field should be absent.