Discrete O(1,4) transformations and new scalar quantum modes on the de Sitter spacetime

TL;DR

The paper explores the symmetry structure of de Sitter spacetime, revealing discrete transformations that relate different quantum modes and expanding understanding of its scalar quantum field modes.

Contribution

It introduces new scalar quantum modes on de Sitter spacetime linked by discrete isometries, enhancing the understanding of its symmetry properties.

Findings

Identification of two Abelian subgroups in de Sitter isometry group.

Discovery of discrete isometry relating different quantum modes.

New scalar quantum modes connected by discrete transformations.

Abstract

It is shown that the isometry group of the de Sitter spacetime includes two different three-dimensional Abelian subgroups which transform between themselves through a discrete isometry corresponding to the time reversal in the five-dimensional Minkowski spacetime embedding the de Sitter one. The eigenfunctions of the generators of these Abelian subgroups form two different sets of quantum modes correlated by the mentioned isometry.