Abstract

It is suggested that the world is locally projectively flat rather than Euclidean. From this postulate it is shown that an (N+1)-particle system has the global geometry of the symmetric spaceSO(4,N+1)/SO(4)×SO(N+1). A complex representation also exists, with structureSU(2,N+1)/S[U(2)×U(N+1)]. Several aspects of these geometrics are developed. Physical states are taken to be eigenfunctions of the Laplace-Beltrami operators. The theory may provide a rational basis for comprehending the groupsSO(4, 2),SU(2)×U(1),SU(3), etc., of current interest