One particle quantum equation in a de Sitter spacetime

TL;DR

This paper derives a quantum equation for a free particle in de Sitter spacetime, utilizing operators linked to the spacetime's symmetries, providing a new perspective on quantum behavior in curved backgrounds.

Contribution

It introduces a novel quantum equation in de Sitter spacetime based on symmetry-related operators independent of space and time coordinates.

Findings

Operators related to Killing vectors are used to formulate the quantum equation.

The approach highlights the role of spacetime symmetries in quantum mechanics.

Provides a framework for analyzing quantum particles in curved spacetime environments.

Abstract

We consider a free particle in a de Sitter spacetime. We use a picture in which the analogs of the Schr\"odinger operators of the particle are independent of both the time and the space coordinates. These operators induce operators which are related to Killing vectors of the de Sitter spacetime.