Infinitesimal generators and quantum operators in de Sitter space

Abstract The 1 + 3-de Sitter space, as a solution of Einstein’s equations, provides a framework for investigating various physical concepts, including quantum mechanics. In this context, the group Sp(2,2) plays a crucial role as the universal covering of the de Sitter space, contributing significantly to the understanding of associated quantum mechanics. In this study, the presentation of infinitesimal generators of the group Sp(2,2) and quantum operators on the de Sitter space is conducted using the coherent states quantization method, also known as Berezin’s quantization method. This approach allows for a systematic examination of the generators and operators within the quantum framework. Furthermore, the exploration of these generators and operators is facilitated by the unitary representation of the principal series of the group Sp(2,2), offering insights into the underlying quantum mechanics principles governing the de Sitter space.