Causality restrictions on relativistic extensions of particle symmetries

Abstract

Relativistic extensions of internal hadron symmetry groups are investigated from the viewpoint of causality requirements. Zeeman's group theoretical definition of causality is adopted and various physically interesting structures of relativistic extensions are studied from the viewpoint of whether they preserve or violate causality. Four theorems that guarantee causality preservation, and three theorems that violate it are deduced. It is concluded that there does not exist a non-trivial coupling of the Poincare group and an internal symmetry group, such asSU(3) orSU(6), preserving causality in a Minkowski space. Extensions in complex or in curved manifolds are briefly discussed.