Localizability in de Sitter space

DOI10.1088/1751-8113/45/36/365401zbMATH Open1266.81020arXiv1011.0901OpenAlexW3106104393MaRDI QIDQ3167565

Publication date: 2 November 2012

Published in: Journal of Physics A: Mathematical and Theoretical (Search for Journal in Brave)

Abstract: An analogue of the Newton-Wigner position operator is defined for a massive neutral scalar field in de Sitter space. The one-particle subspace of the theory, consisting of positive-energy solutions of the Klein-Gordon equation selected by the Hadamard condition, is identified with an irreducible representation of de Sitter group. Postulates of localizability analogous to those written by Wightman for fields in Minkowski space are formulated on it, and a unique solution is shown to exist. A simple expression for the time-evolution of the operator is presented.

Full work available at URL: https://arxiv.org/abs/1011.0901

zbMATH Keywords

quantum mechanics de Sitter space

Mathematics Subject Classification ID

General and philosophical questions in quantum theory (81P05) Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other equations of quantum mechanics (81Q05) Applications of Lie groups to the sciences; explicit representations (22E70) Finite-dimensional groups and algebras motivated by physics and their representations (81R05) Quantum mechanics on special spaces: manifolds, fractals, graphs, lattices (81Q35)