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 lead 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 stressenergy 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.
 Publication:

Journal of High Energy Physics
 Pub Date:
 October 2021
 DOI:
 10.1007/JHEP10(2021)077
 arXiv:
 arXiv:2106.08340
 Bibcode:
 2021JHEP...10..077P
 Keywords:

 Thermal Field Theory;
 Boundary Quantum Field Theory;
 SpaceTime Symmetries;
 High Energy Physics  Theory;
 Condensed Matter  Statistical Mechanics;
 General Relativity and Quantum Cosmology;
 Mathematical Physics;
 Nuclear Theory
 EPrint:
 47 pages, accepted for publication