Quantum spinor field in the FRW universe with a constant electromagnetic background

TL;DR

This paper extends previous work on scalar fields in FRW universes to massive spinor fields, deriving exact solutions, Green functions, and analyzing particle creation and vacuum instability in a universe with a constant electromagnetic background.

Contribution

It provides the first explicit construction of solutions and Green functions for massive spinor fields in this specific cosmological and electromagnetic setting.

Findings

Explicit solutions for Dirac equation in the given background.

Calculation of vacuum-to-vacuum transition amplitude and particle creation.

Analysis of back reaction effects and vacuum polarization.

Abstract

The article is a natural continuation of our paper {\em Quantum scalar field in FRW Universe with constant electromagnetic background}, Int. J. Mod. Phys. {\bf A12}, 4837 (1997). We generalize the latter consideration to the case of massive spinor field, which is placed in FRW Universe of special type with a constant electromagnetic field. To this end special sets of exact solutions of Dirac equation in the background under consideration are constructed and classified. Using these solutions representations for out-in, in-in, and out-out spinor Green functions are explicitly constructed as proper-time integrals over the corresponding contours in complex proper-time plane. The vacuum-to-vacuum transition amplitude and number of created particles are found and vacuum instability is discussed. The mean values of the current and energy-momentum tensor are evaluated, and different approximations for them are presented. The back reaction related to particle creation and to the polarization of the unstable vacuum is estimated in different regimes.