The decomposition of the product of a momentum-zero- and a mass-zero-representation of the Poincaré group

Abstract

The irreducible unitary representations of a twofold covering groupE(2) of the euclidean group of the plane are set up. The product of two irreducible unitary representations ofE(2) and the irreducible unitary representations of SL(2,C) restricted to a subgroupE∼(2) isomorphic toE(2) are reduced to irreducible unitary components. The results are applied to the decomposition of the product of a momentum-zero- and a mass-zero-representation of the proper orthochronous quantummechanical Poincaré group.