Quantization of fields over de Sitter space by the method of generalized coherent states. II. Spinor field

TL;DR

This paper develops a method to quantize spinor fields in de Sitter space using generalized coherent states, linking the Dirac equation with group representations, and derives the corresponding propagator.

Contribution

It introduces a novel approach to quantize spinor fields in de Sitter space via generalized coherent states, connecting group theory with quantum field construction.

Findings

Solutions expressed as products of coherent states

Constructed the quantized Dirac field in de Sitter space

Derived the spinor propagator with an imaginary mass shift

Abstract

Connection of the invariant Dirac equation over the de Sitter space with irreducible representations of the de Sitter group is ascertained. The set of solutions of this equation is obtained in the form of the product of two different systems of generalized coherent states for the de Sitter group. Using these solutions the quantized Dirac field over de Sitter space is constructed and its propagator is found. It is a result of action of some de Sitter invariant spinor operator onto the spin zero propagator with an imaginary shift of a mass.