On representations of the inhomogeneous de Sitter group and on equations of the Schrodinger-Foldy type

Abstract

This paper is a continuation and elaboration of our work quant-ph/0206057 (Nucl. Phys. B, 1968, 7, 79) where some approach to the variable-mass problem were proposed. Here we have found a concret realization of irreducible representations of the inhomogeneous group P(1,n) - the group of translations and rotations in (1+n)-dimensional Minkowski space in two classes (when P_0^2-P_k^2>0 and P_0^2-P_k^2<0). All the P(1,n)-invariant equations of the Schrodinger-Foldy type are written down. Some questions of a physical interpretation of the quantum, mechanical scheme based on the inhomogeneous de Sitter group P(1,n) are discussed.