Induced Representations of Tensors and Spinors of any Rank in the SHP Theory

Abstract

We show that a modification of Wigner's induced representation for the description of a relativistic particle with spin can be used to construct spinors and tensors of arbitrary rank, with invariant decomposition over angular momentum. In particular, scalar and vector fields, as well as the representations of their transformations, are constructed. The method that is developed here admits the construction of wave packets and states of a many body relativistic system with definite total angular momentum. Furthermore, a Pauli-Lubanski operator is constructed on the orbit of the induced representation which provides a Casimir operator for the Poincar\'e group and which contains the physical intrinsic angular momentum of the particle covariantly.