Conformal electrodynamics in curved space

Abstract

We consider the conformal transformation of electrodynamics in curved space. The invariance of the Lorenz gauge condition under the conformal transformation yields the massive Lorenz gauge condition. The conformal massless electrodynamics in curved space yields massive electrodynamics in Minkowski space. The conformal Klein–Gordon equation in the conformal frame is found to yield the quantum Telegraph equation. The conformal transformation of a given field yields the matter (particle) of the field confirming that the field, like a particle, has a dual nature. A special type of conformal transformation is shown to give massless fields a mass that is tantamount to Higgs mechanics. The parameter (weight) ξ=±1 in the conformal transformation of the electromagnetic tensor, F˜μν=Ω±1Fμν, defines the photon mass in the Minkowski frame.