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 applicability of the new form is determined and found to comprise the range of hydrodynamic parameters used in current models of heavy-ion collisions. Moreover, the new definition of the Wigner function leads to the generalized thermodynamic relations for perfect spin hydrodynamics, which were obtained earlier in the approach using the classical concept of spin.