# Relativistic kinetic theory for spin-1/2 particles: Conservation laws, thermodynamics, and linear waves

## TL;DR

This paper develops a comprehensive relativistic kinetic model for spin-1/2 particles, detailing conservation laws, thermodynamics, and linear wave behavior, with implications for quantum plasma physics.

## Contribution

It introduces a fully relativistic kinetic framework for spin-1/2 particles, including conservation laws, thermodynamic equilibrium, and linear dispersion relations, expanding the theoretical understanding of quantum relativistic systems.

## Key findings

- Derived conservation laws for energy, momentum, and angular momentum.
- Provided thermodynamic equilibrium distributions in various limits.
- Calculated linear dispersion relations for coupled spin-momentum eigenfunctions.

## Abstract

We study a recently derived fully relativistic kinetic model for spin-1/2 particles. Firstly, the full set of conservation laws for energy, momentum and angular momentum are given, together with an expression for the (non-symmetric) stress-energy tensor. Next, the thermodynamic equilibrium distribution is given in different limiting cases. Furthermore, we address the analytical complexity that arises when the spin- and momentum eigenfunctions are coupled in linear theory, by calculating the linear dispersion relation for such a case. Finally, we discuss the model and give some context by comparing with potentially relevant phenomena that are not included, such as radiation reaction and vacuum polarization.