Kinetic theory for massive spin-1 particles

TL;DR

This paper develops a kinetic theory framework for massive spin-1 particles, deriving their Wigner function and Boltzmann equation, revealing a doubled Mathisson force and providing evolution equations for their degrees of freedom.

Contribution

It introduces a first-order quantum kinetic formalism for charged spin-1 particles, extending previous spin-1/2 results and capturing their unique dipole effects.

Findings

Wigner function for spin-1 particles derived in electromagnetic fields

Boltzmann equation matches previous spin-1/2 results, with modifications

Mathisson force for spin-1 particles is twice that of spin-1/2

Abstract

We calculate the Wigner function for charged spin-1 particles in inhomogeneous classical electromagnetic fields, going to first order in a power series in $\hbar$. The Boltzmann equation for the scalar distribution function obtained from this formalism agrees with previous calculations for spin-1/2 particles. In particular, we recover a Mathisson force of twice the magnitude, correctly reflecting the higher dipole moment of vector mesons. Evolution equations for vector and tensor degrees of freedom are obtained, and global equilibrium is discussed.