Quantum structures in Einstein general relativity
type: Item
instance of: scholarly article
title: Quantum structures in Einstein general relativity
zbMATH Open document ID: 0977.83009
DOI: 10.1023/A:1007624902983
author: Raffaele Vitolo
published in: Letters in Mathematical Physics
publication date: 2002-01-11T00:00:00Z
review text: The author presents a generalization of the geometric covariant formulation of the Galilei classical mechanics and quantum mechanics on a curved spacetime. This generalization is related to the geometric quantization. He defines an Einstein general relativistic quantum structure in analogy to the known Galilean. This new quantum structure is a Hermitian complex line bundle over spacetime endowed with a universal connection having curvature proportional to the cosymplectic form. The classification and conditions for existence of such structures are shown. They are similar to those of Kostant Souriau. A novel feature is the inclusion of the topology of the spacetime. As examples the author discusses: Minkowski spacetime, Schwarzschild spacetime, Kerr-Newman spacetime, Dirac monopole, the Aharonov-Bohm effect.
Mathematics Subject Classification ID: 83C15
Mathematics Subject Classification ID: 53C05
Mathematics Subject Classification ID: 81S10
Mathematics Subject Classification ID: 53C15
Mathematics Subject Classification ID: 55N05
Mathematics Subject Classification ID: 58A20
Mathematics Subject Classification ID: 14F40
Mathematics Subject Classification ID: 70H40
zbMATH DE Number: 1507911
zbMATH Keywords: Einstein general relativity
zbMATH Keywords: particle mechanics
zbMATH Keywords: jets nonlinear connections cosymplectic forms geometric quantization
zbMATH Keywords: Schwarzschild spacetime
zbMATH Keywords: Kerr-Newman spacetime
zbMATH Keywords: Dirac monopole
Wikidata QID: Q57555749
reviewed by: Andrzej Frydryszak
MaRDI profile type: Publication
full work available at URL: a:1007624902983
OpenAlex ID: W183405983
description: scientific article; zbMATH DE number 1507911