Parametrizing relativistic quantum mechanics

Abstract

Galilean time in nonrelativistic quantum theory and historical time in parametrized relativistic quantum theories such as the four-space formulation are examined. Clear physical distinctions are drawn between Galilean time, Minkowski time, and historical time. Minkowski time is the temporal coordinate of a space-time four-vector. Galilean time and historical time are evolution (ordering) parameters in their respective theoretical frameworks. Using N-body formulations, a physically unambiguous procedure for measuring evolution parameters in terms of familiar observables is presented. The procedure is illustrated by the design of a simple evolution-parameter clock.