Tensor fields invariant under subgroups of the conformal group of space-time

Abstract

This work is concerned with the characterization of tensor fields in (compactified) Minkowski space which are invariant under the action of subgroups of the conformal group. The general method for determining all invariant fields under the smooth action of a Lie group G on a manifold M is given, both in global and in local form. The maximal subgroups of the conformal group are divided into conjugacy classes under the Poincaré group and the most general fields of 1-forms, 2-forms, symmetric (0,2) tensors and scalar densities which are invariant under representatives of each class (as well as certain other subgroups) are then determined. The results are then discussed from the viewpoint of physical interpretation (as, e.g., electromagnetic fields, metric tensors, etc.) and applicability; in particular, for studies of spontaneously or otherwise broken conformal invariance.