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

TL;DR

This paper derives exact analytical forms of key quantum field theoretical quantities for massless Dirac fields at equilibrium with rotation and acceleration, extending previous scalar field results and providing new insights into fermionic current behaviors.

Contribution

It introduces a novel iterative and analytic continuation method to obtain exact solutions for Dirac fields under combined rotation and acceleration, extending prior scalar field analyses.

Findings

Mean values match known results in special cases

New expressions for combined rotation and acceleration

Currents vanish at Unruh temperature in pure acceleration case

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.