An exact solution of the Currie–Hill equations in 1+1 dimensional Minkowski space

Abstract

We present an exact two-particle solution of the Currie–Hill equations of Predictive Relativistic Mechanics in 1 + 1 dimensional Minkowski space. The instantaneous accelerations are given in terms of elementary functions depending on the relative particle position and velocities. The general solution of the equations of motion is given and by studying the global phase space of this system it is shown that this is a subspace of the full kinematic phase space. • Explicit solution of the 1 + 1 dimensional Currie–Hill equations. • Explicit solution of the equations of motion. • Explicit construction of the Poincaré generators. • Detailed description of the global structure of the phase space.