The free Dirac spinors of the spin basis on the de Sitter expanding universe

TL;DR

This paper investigates the behavior of free Dirac spinors in the de Sitter universe, showing how phase factors influence their global properties and defining modes that are well-behaved even at rest, with implications for quantum field quantization.

Contribution

It introduces a method to construct Dirac spinor modes on de Sitter space using phase functions, ensuring well-defined modes at rest and clarifying their quantization structure.

Findings

Defined phase functions for Dirac modes on de Sitter space

Established modes well-defined at rest in local charts

Clarified the form of the energy operator in quantization

Abstract

It is shown that on the de Sitter space-time the global behavior of the free Dirac spinors in momentum representation is determined by several phases factors which are functions of momentum with special properties. Such suitable phase functions can be chosen for writing down the free Dirac quantum modes of the spin basis that are well-defined even for the particles at rest in the moving local charts where the modes of the helicity basis remain undefined. Under quantization these modes lead to a basis in which the one-particle operators keep their usual forms apart from the energy operator which lays out a specific term which depend on the concrete phase function one uses.