Stargenfunctions, generally parametrized systems and a causal formulation of phase space quantum mechanics

TL;DR

This paper explores the application of quantum phase space methods to generally parametrized systems with a natural time variable, demonstrating a causal representation of quantum quasidistributions in such systems.

Contribution

It introduces a causal formulation of phase space quantum mechanics for parametrized systems, highlighting the potential of quantum phase space methods in constrained and covariant systems.

Findings

Causal representation of quantum phase space quasidistributions achieved

Illustrates potential of phase space methods in constrained systems

Provides pedagogical example of deformation quantization in parametrized systems

Abstract

We address the deformation quantization of generally parametrized systems displaying a natural time variable. The purpose of this exercise is twofold: first, to illustrate through a pedagogical example the potential of quantum phase space methods in the context of constrained systems and particularly of generally covariant systems. Second, to show that a causal representation for quantum phase space quasidistributions can be easily achieved through general parametrization. This result is succinctly discussed.