Unitary Representations of the Homogeneous Lorentz Group in an O(1,1)⊗O(2) Basis and Some Applications to Relativistic Equations

Abstract

Unitary irreducible representations of the homogeneous Lorentz group O(3, 1) belonging to the principal series are reduced with respect to the subgroup O(1,1) ⊗ O(2). As an application we determine the mixed basis matrix elements between O(3) and O(1,1) ⊗ O(2) bases and derive recurrence relations for them. This set of functions is then used to obtain invariant expansions of solutions of the Dirac and Proca free field equations. These expansions are shown to have the correct nonrelativistic limit.