Local equilibrium Wigner function for spin-1/2 particles
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.
Cite
@article{arxiv.2505.02657,
title = {Local equilibrium Wigner function for spin-1/2 particles},
author = {Samapan Bhadury and Zbigniew Drogosz and Wojciech Florkowski and Sudip Kumar Kar and Valeriya Mykhaylova},
journal= {arXiv preprint arXiv:2505.02657},
year = {2025}
}
Comments
Significantly revised version including discussion of the nonlinear causality and stability of spin hydrodynamics based on the new formula for the Wigner function