Concept of a kinematical stability group in implementing relativistic symmetry

The concept of a kinematical stability group is discussed, which, for an arbitrary four-momentum organized the set of p irreducible representations coherently into an irreducible representation of a larger symmetry group. In terms of a no-go theorem, such a larger symmetry is implementable only as an infinite dimensional group. These ideas arose through an attempt to understand and interpret Dirac's positive energy relativistic wave equation. It was found that the Dirac construction could in fact be viewed as a form of a positive energy relativistically covariant oscillator. This led to the concept of a kinematic stability group. 27 references