Lorentz symmetries in a doubly hyperbolic phase space: The connection with Minkowski four-space

Abstract

The phase space kinematics of a hyperbolic position space combined with the velocity-momentum space of special relativity is shown to be compatible with the Minkowski four-space description of position and local time. The transformation between the Minkowski coordinates and those of the curvilinear hyperbolic system is given, and the implications of the two viewpoints for Lorentz symmetry are reviewed.