Massless fields over $R^1 \times H^3$ space-time and coherent states for the Lorentz group

TL;DR

This paper derives solutions for massless arbitrary-spin fields on a specific curved spacetime using Lorentz group coherent states and constructs their invariant propagators, including an explicit scalar propagator expression.

Contribution

It introduces a method to obtain solutions for massless fields of any spin on ${\bf R}^1 \times H^3$ using generalized Lorentz coherent states and constructs invariant propagators.

Findings

Explicit solutions for massless fields of arbitrary spin on ${\bf R}^1 \times H^3$

Construction of invariant propagators for these fields

Explicit expression for the scalar propagator

Abstract

The solutions of the arbitrary-spin massless wave equations over ${\bf R}^1 \times H^3$ space are obtained using the generalized coherent states for the Lorentz group. The use of these solutions for the construction of invariant propagators of quantized massless fields with an arbitrary spin over the ${\bf R}^1 \times H^3$ space is considered. The expression for the scalar propagator is obtained in the explicit form.