Group contraction in a fiber bundle with Cartan connection

Abstract

A contraction of the structural group with respect to the stability subgroup is performed in a fiber bundle with Cartan connection. The relation of the connections in the original and in the contracted bundle is examined. As an example interesting for physics the contraction of the SO(4,1) de Sitter bundle over space–time to the affine tangent bundle over space–time is discussed with the latter bundle possessing the Poincaré group as structural group.