Internal space-time symmetries of massive and massless particles

Abstract

A unified description is given for internal space-time symmetries for massive and massless particles. It is noted that the little groups governing the internal symmetries of massive and massless particles are locally isomorphic to the three-dimensional rotation group or O(3) and the two-dimensional rotation group or E(2), respectively. It is noted also that the E(2) group can be obtained from a large-radius/flat-surface approximation of O(3). This procedure is then shown to be directly applicable to that of obtaining the E(2)-like little group for massless particles from the O(3)-like little group for massive particles in the infinite-momentum/zero-mass limit.