Wavepackets on de Sitter spacetime

TL;DR

This paper constructs and analyzes wavepackets on de Sitter spacetime, showing their asymptotic behavior and convergence to Minkowski spacetime wavepackets as the de Sitter radius increases.

Contribution

It introduces a method to construct wavepackets on de Sitter spacetime using Casimir eigenvalues and analyzes their asymptotic properties and Minkowski limit.

Findings

Wavepackets on de Sitter spacetime are constructed using Casimir eigenvalues.

As the de Sitter radius approaches infinity, wavepackets converge to Minkowski spacetime wavepackets.

Plane waves in the limit are supported sharply on the mass shell.

Abstract

We construct wavepackets on de Sitter spacetime, with masses consistently defined from the eigenvalues of an irreducible representation of a Casimir element in the universal enveloping algebra of the Lorentz algebra and analyse their asymptotic behaviour. Furthermore, we show that, in the limit as the de Sitter radius tends to infinity, the wavepackets tend to the wavepackets of Minkowski spacetime and the plane waves arising after contraction have support sharply located on the mass shell.