Polarized Dirac fermions in de Sitter spacetime

TL;DR

This paper develops a gauge-invariant framework for the Dirac field in de Sitter spacetime, deriving solutions and quantization methods that clarify the behavior of polarized fermions in this curved background.

Contribution

It introduces a gauge-invariant approach to Dirac fields in de Sitter spacetime, identifying symmetry operators and deriving explicit plane wave solutions.

Findings

Operators commuting with the Dirac operator are identified.

Explicit plane wave solutions with momentum and helicity are derived.

Canonical quantization yields consistent physical interpretations.

Abstract

The tetrad gauge invariant theory of the free Dirac field in two special moving charts of the de Sitter spacetime is investigated pointing out the operators that commute with the Dirac one. These are the generators of the symmetry transformations corresponding to isometries that give rise to conserved quantities according to the Noether theorem. With their help the plane wave spinor solutions of the Dirac equation with given momentum and helicity are derived and the final form of the quantum Dirac field is established. It is shown that the canonical quantization leads to a correct physical interpretation of the massive or massless fermion quantum fields.