Simulation of classical particle trajectories in a complex two-dimensional space

Abstract

Classical particles of arbitrary rest mass and spin are modeled in a two-dimensional space C2 (which has two complex coordinates ξA, A=1, 2) in the following way. It is first shown that a preferred set of trajectories ξA=ζA(s), designated geodesics, can be introduced from a variation principle that makes stationary the real variable s. The latter plays the role of proper time and serves to parametrize the trajectories. The geodesics so defined are then shown to be associated with a nonlinear representation of the Poincaré group. A set of Poincaré vectors and tensors are constructed from ζA and its proper time derivatives and these simulate the properties of the position, momentum, angular momentum, and internal angular momentum variables of a classical massive particle of arbitrary spin.