Vector and tensor fields on conformal space

Abstract

We consider in this paper vector and tensor fields on the compactified Minkowski space M4c and investigate their transformation properties under the group SO (2,4) of conformal transformations which are well defined on the manifold M4c contrary to their singular behavior on the pseudo−Euclidean noncompact Minkowski space M4. In writing down field equations on the manifold M4c, we get immediately the well−known conformal invariance of Maxwell’s equations. Also the problem of gauge transformations of the vector potential is treated both from the global point of view on the manifold M4c and from the local point of view on the Minkowski space M4. There we show which gauge instead of the so−called Lorentz gauge one has to choose to get a conformal covariant formulation of Maxwell’s equations on the pseudo−Euclidean noncompact Minkowski space M4.