Projective Representations and the Relation of Internal to Space-Time Symmetries

Abstract

The relation of space-time to internal symmetries in relativistic quantum mechanics is investigated using the Mackey theory of induced projective representations of group extensions. Representation multipliers are found for semidirect products of the Poincaré group and arbitrary internal symmetry groups. Upon investigating a typical example, it is found that when relations such as UπUC=(−1)2J UCUπ, obtained from field theory, are assumed, a unique choice of representation multiplier follows; in particular, this multiplier requires UCπt2=1 for all J. Representations relative to this multiplier are computed.