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

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.

Spin polarization evolution in a boost-invariant hydrodynamical background

“…These forms have been chosen in such a way as to obtain the simplest possible description which is self-consistent from the thermodynamic and hydrodynamic point of view. A more recent work has demonstrated, however, that other forms of the energymomentum and/or spin tensors should be used if we want to connect them with the underlying kinetic theory [36], see also [37,38]. As a matter of fact, these forms agree with those introduced by de Groot, van Leeuwen, and van Weert (GLW) in Ref.…”