Space-time geometry of relativistic particles in four-dimensional phase space

Abstract

The Wigner phase-space picture of Dirac’s two-oscillator representation of O(3,2) is given. This constitutes a real representation of Sp(4) which allows us to study the symmetry of the O(3,2) de Sitter group using canonical transformations in four-dimensional phase space. It is also possible to study subgroups of O(3,1) in this phase space. The phase-space picture is given for the two-oscillator model of van Dam, Ng, and Biedenharn [Phys. Lett. B 158, 227 (1985)] for the little groups for massive and massless particles. In this formalism, Lorentz transformations can be described in terms of canonical transformations in phase space. It is particularly convenient for studying infinite-momentum/zero-mass limit of the O(3)-like little group for a massive particle. It is shown that the trivial representation of the E(2)-like little group for a massless particle emerges from this limiting process. The origin of gauge degree of freedom is discussed.