Semi-classical kinetic theory for massive spin-half fermions with leading-order spin effects

TL;DR

This paper develops a semi-classical kinetic theory framework for massive spin-half fermions, incorporating leading-order spin effects at both classical and quantum levels, and provides a basis for spin hydrodynamics.

Contribution

It introduces a generalized dynamical equation for spin-half fermions using Wigner functions and semi-classical expansion, enabling the study of spin effects in kinetic and hydrodynamic regimes.

Findings

Derivation of a generalized Boltzmann-like equation including spin effects

Framework for collision kernels with local and non-local interactions

Foundation for spin hydrodynamics conserving energy-momentum and angular momentum

Abstract

We consider the quantum kinetic-theory description for interacting massive spin-half fermions using the Wigner function formalism. We derive a general kinetic theory description assuming that the spin effects appear at the classical and quantum level. To track the effect of such different contributions we use the semi-classical expansion method to obtain the generalized dynamical equations including spin, analogous to classical Boltzmann equation. This approach can be used to obtain a collision kernel involving local as well as non-local collisions among the microscopic constituent of the system and eventually, a framework of spin hydrodynamics ensuring the conservation of the energy-momentum tensor and total angular momentum tensor.