Spin kinetic theory - quantum kinetic theory in extended phase space

TL;DR

This paper develops a quantum kinetic theory incorporating particle spin in an extended phase space, introducing a scalar quasi-distribution function that remains positive definite and closely relates to Husimi functions, with implications for gauge issues and fluid hierarchies.

Contribution

It presents a novel scalar quasi-distribution function for spin-1/2 particles using a spin projection operator, differing from traditional Wigner functions, and connects quantum optics concepts to kinetic theory.

Findings

The scalar quasi-distribution function is positive definite.

A close relation to Husimi functions is established.

The approach addresses gauge issues and fluid moment hierarchies.

Abstract

The concept of phase space distribution functions and their evolution is used in the case of en enlarged phase space. In particular, we include the intrinsic spin of particles and present a quantum kinetic evolution equation for a scalar quasi-distribution function. In contrast to the proper Wigner transformation technique, for which we expect the corresponding quasi-distribution function to be a complex matrix, we introduce a spin projection operator for the density matrix in order to obtain the aforementioned scalar quasi-distribution function. There is a close correspondence between this projection operator and the Husimi (or Q) function used extensively in quantum optics. Such a function is based on a Gaussian smearing of a Wigner function, giving a positive definite distribution function. Thus, our approach gives a Wigner-Husimi quasi-distribution function in extended phase space, for which the reduced distribution function on the Bloch sphere is strictly positive. We also discuss the gauge issue and the fluid moment hierarchy based on such a quantum kinetic theory.