Relativistic diffusion of elementary particles with spin

TL;DR

This paper generalizes relativistic diffusion to include particles with spin, linking classical diffusion equations to quantum Wigner functions and exploring gauge freedoms, electromagnetic effects, and equilibrium states.

Contribution

It introduces a novel relativistic diffusion equation for spinning particles, incorporating gauge freedom and fiber bundle geometry, extending previous models for spinless particles.

Findings

Derived a diffusion equation for particles with spin.

Analyzed gauge freedom associated with Wigner rotations.

Discussed effects of electromagnetic fields and equilibrium states.

Abstract

We obtain a generalization of the relativistic diffusion of Schay and Dudley for particles with spin. The diffusion equation is a classical version of an equation for the Wigner function of an elementary particle. The elementary particle is described by a unitary irreducible representation of the Poincare group realized in the Hilbert space of wave functions in the momentum space. The arbitrariness of the Wigner rotation appears as a gauge freedom of the diffusion equation. The spin is described as a connection of a fiber bundle over the momentum hyperbolic space (the mass-shell). Motion in an electromagnetic field, transport equations and equilibrium states are discussed.