Canonical Gauges in the Path Integral for Parametrized Systems

TL;DR

This paper demonstrates how to transform parametrized systems into ordinary gauge systems using canonical transformations, enabling the use of canonical gauges in path integral quantization when an intrinsic global time exists.

Contribution

It introduces a method to construct canonical transformations that convert parametrized systems into ordinary gauge systems suitable for path integral quantization.

Findings

Canonical transformations can turn parametrized systems into ordinary gauge systems.

This approach requires the Hamiltonian constraint to admit an intrinsic global time.

The method enables the use of canonical gauges in path integral formulations.

Abstract

It is well known that --differing from ordinary gauge systems-- canonical gauges are not admissible in the path integral for parametrized systems. This is the case for the relativistic particle and gravitation. However, a time dependent canonical transformation can turn a parametrized system into an ordinary gauge system. It is shown how to build a canonical transformation such that the fixation of the new coordinates is equivalent to the fixation of the original ones; this aim can be achieved only if the Hamiltonian constraint allows for an intrinsic global time. Thus the resulting action, describing an ordinary gauge system and allowing for canonical gauges, can be used in the path integral for the quantum propagator associated with the original variables.