Relativistic extension of non-compact symmetry groups

Abstract

The problem of relativistieally boosting the unitary representations of a non-compact spin-containing rest-symmetry group is solved by starting with non-unitary infinite-dimensional representations of a relativistic extension of this group, by adjoining to this extension four space-time translations and by the napplying Bargmann-Wigner equations to guarantee aunitary norm. The procedure has similarities to the conventional method of induced representations. The boosting problem considered here is the first step towards the solution of the problem of coupling of such infinite-dimensional representations which is also briefly investigated. Startin g from a rest-symmetry like U (6,6) a chain of subgroups GL (6), U (3,3), etc., is exhibited for collinear and coplanar processes, etc.