Deformation Quantization and Wigner Functions

TL;DR

This paper reviews the Weyl-Wigner phase space formulation of quantum mechanics, exploring Wigner functions, their properties, boundary effects, and environment-induced decoherence within this framework.

Contribution

It provides a comprehensive review of the Weyl-Wigner formalism, including conditions for Wigner functions and effects of boundaries and decoherence, offering new insights into phase space quantum mechanics.

Findings

Necessary and sufficient conditions for Wigner functions identified

Analysis of boundary effects on Wigner distributions conducted

Discussion of environment-induced decoherence in phase space

Abstract

We review the Weyl-Wigner formulation of quantum mechanics in phase space. We discuss the concept of Narcowich-Wigner spectrum and use it to state necessary and sufficient conditions for a phase space function to be a Wigner distribution. Based on this formalism we analize the modifications introduced by the presence of boundaries. Finally, we discuss the concept of environment-induced decoherence in the context of the Weyl-Wigner approach.