Magnetic Monopole and the Finite Photon Mass: Are They Compatible?

Abstract

We analyze the role played by the gauge invariance for the existence of Dirac monopole. To this end, we consider the electrodynamics with massive photon and ask if the magnetic charge can be introduced there. We show that the derivation of the Dirac quantization condition based on the angular momentum algebra cannot be generalized to the case of massive electrodynamics. Possible implications of this result are briefly discussed.