Time dependent transformations in deformation quantization

TL;DR

This paper develops a fully invariant formalism for phase space quantum mechanics under time-dependent transformations, enabling new representations and a causal approach to Wigner quantum mechanics.

Contribution

It introduces a covariant, invariant formalism for phase space quantum mechanics under time-dependent transformations, expanding the framework's flexibility.

Findings

Enlarged set of phase space representations.

Constructed a causal representation for Wigner quantum mechanics.

Formalism invariant under standard and time-dependent coordinate transformations.

Abstract

We study the action of time dependent canonical and coordinate transformations in phase space quantum mechanics. We extend the covariant formulation of the theory by providing a formalism that is fully invariant under both standard and time dependent coordinate transformations. This result considerably enlarges the set of possible phase space representations of quantum mechanics and makes it possible to construct a causal representation for the distributional sector of Wigner quantum mechanics.