Wigner function approach to polarization-vorticity coupling and hydrodynamics with spin

TL;DR

This paper develops a Wigner function framework for particles with spin to explore the relationship between thermal vorticity and spin polarization, deriving hydrodynamic equations with spin in local equilibrium.

Contribution

It introduces a new equilibrium Wigner function approach for spin-1/2 particles and formulates hydrodynamic equations with spin in local equilibrium within different theoretical frameworks.

Findings

Thermal-vorticity and spin polarization tensors are constant in global equilibrium.

Hydrodynamic equations with spin are derived for local equilibrium.

GLW and canonical formalisms are related by a pseudo-gauge transformation.

Abstract

Newly introduced equilibrium Wigner functions for particles with spin one-half are used in the semi-classical kinetic equations to study a possible relation between thermal vorticity and spin polarization. It is shown that in global equilibrium both the thermal-vorticity and spin polarization tensors are constant but not necessarily equal. In the case of local equilibrium, we define a procedure leading to hydrodynamic equations with spin. We introduce such equations for the de~Groot, van~Leeuwen, and van~Weert (GLW) formalism as well as for the canonical scheme (these two frameworks differ by the definitions of the energy-momentum and spin tensors). It is found that the GLW and canonical versions are connected by a pseudo-gauge transformation.