Quantization of fields over de Sitter space by the method of generalized coherent states

TL;DR

This paper develops a method to quantize scalar and Dirac fields over de Sitter space using generalized coherent states, deriving invariant propagators and establishing their properties like invariance and causality.

Contribution

It introduces a novel approach to quantize fields on de Sitter space via generalized coherent states, connecting group representations with field solutions.

Findings

Constructed invariant propagators for scalar and Dirac fields.

Demonstrated de Sitter invariance and causality of the propagators.

Linked Dirac equation solutions to irreducible de Sitter group representations.

Abstract

A system of generalized coherent states for the de Sitter group obeying the Klein-Gordon equation and corresponding to the massive spin zero particles over the de Sitter space is considered. This allows us to construct the quantized scalar field by the resolution over these coherent states; the corresponding propagator is computed by the method of analytic continuation to the complex de Sitter space and coincides with expressions obtained previously by other methods. Considering the case of spin 1/2 we establish the connection of the invariant Dirac equation over the de Sitter space with irreducible representations of the de Sitter group. 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. We show that the constructed propagators possess the de Sitter-invariance and causality properties.