QUANTIZATION OF KINEMATICS ON CONFIGURATION MANIFOLDS

DOI10.1142/S0129055X0100079XzbMath1029.81043arXivmath-ph/0104013MaRDI QIDQ4418299

H. D. Doebner, J. Tolář, Pavel Šťovíček

Publication date: 7 August 2003

Published in: Reviews in Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math-ph/0104013

zbMATH Keywords

external gauge fieldimprimitivity systemsBorel quantizationgeneralized positions and momenta

Mathematics Subject Classification ID

General and philosophical questions in quantum theory (81P05) Applications of Lie groups to the sciences; explicit representations (22E70) Geometry and quantization, symplectic methods (81S10) Commutation relations and statistics as related to quantum mechanics (general) (81S05) Differential geometric methods, including holonomy, Berry and Hannay phases, Aharonov-Bohm effect, etc. in quantum theory (81Q70) Induced representations for locally compact groups (22D30)

Related Items

QUANTIZATION METHODS: A GUIDE FOR PHYSICISTS AND ANALYSTS ⋮ Group theoretical derivation of the minimal coupling principle ⋮ Non-abelian quantum statistics on graphs ⋮ Quantum charges and spacetime topology: the emergence of new superselection sectors ⋮ Quantum models of classical world ⋮ On quantum mechanics of \(n\)-particle systems on 2-manifolds -- a case study in topology ⋮ Manifold topology, observables, and gauge group

Cites Work

• Unitary representations of group extensions. I
• Systems of imprimitivity for the group of diffeomorphisms
• Deformation theory and quantization. I: Deformations of symplectic structures
• Scattering on a finite chain of vortices
• On the existence of a connection with curvature zero
• Quantization of Nonlinear Systems
• Significance of Electromagnetic Potentials in the Quantum Theory
• Induced representations of the group of diffeomorphisms of R³
• Particle statistics from induced representations of a local current group
• Quantum mechanics on homogeneous spaces
• Quantised singularities in the electromagnetic field,
• Borel quantum kinematics of rank k on smooth manifolds
• On topological effects in quantum mechanics: The harmonic oscillator in the pointed plane

This page was built for publication: QUANTIZATION OF KINEMATICS ON CONFIGURATION MANIFOLDS