Exact equilibrium distributions in statistical quantum field theory with rotation and acceleration: Dirac field

Abstract

We derive the general exact forms of the Wigner function, of mean values of conserved currents, of the spin density matrix, of the spin polarization vector and of the distribution function of massless particles for the free Dirac field at global thermodynamic equilibrium with rotation and acceleration, extending our previous results obtained for the scalar field. The solutions are obtained by means of an iterative method and analytic continuation, which leads to formal series in thermal vorticity. In order to obtain finite values, we extend to the fermionic case the method of analytic distillation introduced for bosonic series. The obtained mean values of the stress-energy tensor, vector and axial currents for the massless Dirac field are in agreement with known analytic results in the special cases of pure acceleration and pure rotation. By using this approach, we obtain new expressions of the currents for the more general case of combined rotation and acceleration and, in the pure acceleration case, we demonstrate that they must vanish at the Unruh temperature.

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

“…where W A and w are defined as in Eq.s ( 25) and ( 24), except that the thermal vorticity does not have to be constant anymore. The second term in (45) is the axial current induced by the thermal shear ξ and from the Wigner function evaluated in [5] we can show that…”

“…( 3), the only difference being that at global equilibrium the thermal vorticity must be a constant tensor. For the spin polarization at all order of thermal vorticity see [45].…”