Pseudogauge dependence of the spin polarization and of the axial vortical effect

Abstract

The mean spin polarization vector of spin 1/2 particles in a relativistic fluid at local thermal equilibrium (LTE) in different pseudogauges (PGs), i.e., with different choices for the decomposition of orbital and spin angular momentum, is obtained. The spin polarization obtained in the canonical PG differs from the one obtained in the Belinfante PG. It is found that this difference can not be written by replacing the thermal vorticity with the spin potential in the usual polarization formula. Other PG choices affect the contribution of thermal shear to the spin polarization. Therefore, the choice of a PG affects the predictions for the polarization measured in heavy-ion collisions. In general, it is shown that the Wigner function of a noninteracting Dirac field at LTE is affected by the PG transformations. Explicit expressions of the mean axial current are also calculated and it is found that even the axial vortical effect conductivity depends on the PG.