On the \({\mit \Theta }\)-term in Electrodynamics
Pawel O. Mazur (Department of Physics and Astronomy, University of South Carolina, Columbia, SC 29208, USA); Andrzej Staruszkiewicz (Faculty of Physics, Astronomy and Applied Computer Science, S. Łojasiewicza 11, 30-348 Kraków, Poland)
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.