Quantization of massless fields over the static Robertson-Walker space of constant negative curvature

TL;DR

This paper develops a new method for quantizing massless fields of arbitrary spin over the ${\Bbb R}^1 \times H^3$ space, constructing explicit propagators that are invariant and causal, advancing quantum field theory in curved spacetimes.

Contribution

It introduces a novel quantization approach for massless fields on symmetric spaces, providing explicit propagators for spin 0 and 1/2 fields over ${\Bbb R}^1 \times H^3$.

Findings

Propagators are invariant under ${\Bbb R}^1 \times SO(3,1)$.

Explicit forms of propagators for spin 0 and 1/2 fields are derived.

The method applies to arbitrary spin fields on symmetric curved spaces.

Abstract

Taking the ${\Bbb R}^1 \times H^3$ space as an example, we develop the new method of quantization of fields over symmetric spaces. We construct the quantized massless fields of an arbitrary spin over the ${\Bbb R}^1 \times H^3$ space by the resolution over the systems of "plane waves" which are solutions of the corresponding wave equations. The propagators of these fields are ${\Bbb R}^1 \times SO(3,1)$-invariant and causal. For spin 0 and 1/2 fields the propagators are obtained in the explicit form.