Local equilibrium Wigner function for spin-1/2 particles

TL;DR

This paper introduces a new form of the local equilibrium Wigner function for spin-1/2 particles, ensuring proper normalization of spin polarization and leading to consistent thermodynamic relations in relativistic spin hydrodynamics.

Contribution

It proposes a revised expression for the local equilibrium Wigner function that improves normalization and stability in relativistic spin hydrodynamics.

Findings

New Wigner function form satisfies normalization of mean spin polarization.

Derived thermodynamic relations are consistent with classical spin concepts.

Proved nonlinear causality and stability of the new hydrodynamics.

Abstract

Formal connections between the spin density matrix and the Wigner function for spin-1/2 particles forming a relativistic gas are explored to determine their general structures. They suggest that the commonly used form of the local equilibrium Wigner function should be replaced by a new expression. The latter fulfills the necessary condition for the normalization of the mean spin polarization, which the former fails to reproduce. The new definition of the Wigner function leads to generalized thermodynamic relations for perfect spin hydrodynamics, identical to those obtained earlier using the classical concept of spin. Moreover, one can prove that the perfect spin hydrodynamics based on the new equilibrium Wigner function is nonlinearly causal and stable. Finally, the selection rule for the Lagrange multipliers, which is satisfied by real systems, is discussed.