# Kinetic theory for massive spin-1/2 particles from the Wigner-function formalism

## TL;DR

This paper derives a kinetic theory for massive spin-1/2 particles using the Wigner-function formalism, incorporating electromagnetic interactions, and explores implications for relativistic heavy-ion collisions.

## Contribution

It extends the Wigner-function approach to include inhomogeneous electromagnetic fields and derives a generalized Boltzmann equation with dipole force effects.

## Key findings

- Derived the Wigner function for massive spin-1/2 particles in electromagnetic fields.
- Established a generalized Boltzmann equation including dipole forces.
- Connected the framework to polarization effects in heavy-ion collisions.

## Abstract

We calculate the Wigner function for massive spin-1/2 particles in an inhomogeneous electromagnetic field to leading order in the Planck constant $\hbar$. Going beyond leading order in $\hbar$ we then derive a generalized Boltzmann equation in which the force exerted by an inhomogeneous electromagnetic field on the particle dipole moment arises naturally. Carefully taking the massless limit we find agreement with previous results. The case of global equilibrium with rotation is also studied. Finally, we outline the derivation of fluid-dynamical equations from the components of the Wigner function. The conservation of total angular momentum is promoted as an additional fluid-dynamical equation of motion. Our framework can be used to study polarization effects induced by vorticity and magnetic field in relativistic heavy-ion collisions.