Representation theory of the universal covering of the Euclidean conformal group and conformal invariant Green’s functions

Abstract

We present a special realization for the universal covering of the Euclidean conformal group. This group can be defined as a transformation group on the Euclidean version of compactified Minkowski space such that the action on this space coincides with the usual one of the Euclidean conformal group. We construct the representations of the principal and complementary series and derive the intertwining kernels for the equivalent representations. The connection between representation theory and conformal invariant quantum field theory is studied. To this end we also give the reduction of the tensor product of two representations of the supplementary series.