Towards a CPT Invariant Quantum Field Theory on Elliptic de Sitter Space

TL;DR

This paper explores a CPT-invariant quantum field theory on elliptic de Sitter space, demonstrating how antipodal identification affects field solutions, global properties, and observer information completeness.

Contribution

It introduces a framework for quantum fields on elliptic de Sitter space with CPT invariance, including exact solutions and conditions for spinor existence.

Findings

Existence of globally defined spinors under certain conditions.

Explicit solutions for scalar and spinor fields in Beltrami coordinates.

CPT invariance established for quantum field theory on elliptic de Sitter space.

Abstract

Consequences of Schr\"{o}dinger's antipodal identification on quantum field theory in de Sitter space are investigated. The elliptic $\mathbb{Z}_2$ identification provides observers with complete information. We show that a suitable confinement on dimension of the elliptic de Sitter space guarantees the existence of globally defined spinors and orientable $dS/\mathbb{Z}_2$ manifold. In Beltrami coordinates, we give exact solutions of scalar and spinor fields. The CPT invariance of quantum field theory on the elliptic de Sitter space is presented explicitly.