Is it possible to accommodate massive photons in the framework of a gauge-invariant electrodynamics?

The construction of an alternative electromagnetic theory that preserves Lorentz and gauge symmetries, is considered. We start off by building up Maxwell electrodynamics in (3+1)D from the assumption that the associated Lagrangian is a gauge- invariant functional that depends on the electron and photon fields and their first derivatives only. In this scenario, as well- known, it is not possible to set up a Lorentz invariant gauge theory containing a massive photon. We show nevertheless that there exist two radically different electrodynamics, namely, the Chern- Simons and the Podolsky formulat...