Gauge-independent Husimi functions of charged quantum particles in the electro-magnetic field

TL;DR

This paper introduces gauge-independent Husimi functions for charged quantum particles in electromagnetic fields, providing explicit operators and evolution equations, enhancing the analysis of quantum states in gauge-invariant frameworks.

Contribution

It presents a novel gauge-independent Husimi function using the Stratonovich-Wigner approach, with explicit operators and evolution equations, advancing quantum phase space methods.

Findings

Explicit gauge-independent Husimi functions derived.

Dequantizers and quantizers explicitly constructed.

Evolution equations for the gauge-independent Husimi functions obtained.

Abstract

Gauge-independent Husimi function ($Q-$function) of states of charged quantum particles in the electro-magnetic field is introduced using the gauge-independent Stratonovich-Wigner function, the corresponding dequantizer and quantizer operators transforming the density matrix of state to the Husimi function and vice versa are found explicitly, and the evolution equation for such function is derived. Also own gauge-independent non-Stratonovich Wigner function is suggested and its Husimi function is obtained. Dequantizers and quantizers for these Wigner and Husimi functions are given.