Nontrivial \(U(1)\) bundles over tori and properties of many-particle systems with topological charge
type: Item
instance of: scholarly article
title: Nontrivial \(U(1)\) bundles over tori and properties of many-particle systems with topological charge
zbMATH Open document ID: 0804.58066
DOI: 10.1007/BF01074109
author: O. M. Ivanov
author: A. G. Savinkov
published in: Theoretical and Mathematical Physics
publication date: 1994-07-13T00:00:00Z
review text: In parallel with the Wu-Yang treatment of singularities of Dirac's charge-monopole system the authors of the present paper consider the dynamics of special type many-particle system over non-trivial \(U(1)\)- bundles and prove that: i) every attempt for launching the dynamics over the base manifold leads to singularities of the wave function; ii) these many-particle configurations are stable (by topological reasons); iii) transposition operator for identical particles inside the total space does not exist. The paper ends with an interesting Appendix in which the existing classification results in the geometry of simply-connected three- dimensional manifolds are shortly reviewed and the point of contact with the present work is discussed.
Mathematics Subject Classification ID: 58Z05
Mathematics Subject Classification ID: 81T13
Mathematics Subject Classification ID: 57N10
Mathematics Subject Classification ID: 53C80
zbMATH DE Number: 589588
zbMATH Keywords: topological invariants
zbMATH Keywords: any on statistics
zbMATH Keywords: many-particle systems
reviewed by: Ivaïlo Mladenov
MaRDI profile type: Publication
cites work: Quantised singularities in the electromagnetic field,
cites work: Hyperbolic structures on 3-manifolds. I: Deformation of acylindrical manifolds
cites work: Three dimensional manifolds, Kleinian groups and hyperbolic geometry
cites work: Q4692272
cites work: Q5731354
cites work: SCATTERING, GREEN’S FUNCTIONS AND SYMMETRIES IN A TOTAL SPACE OF A DIRAC MONOPOLE FIBRE BUNDLE
cites work: Discrete symmetries of monopole bundles
cites work: Q3994693
cites work: Flux quantization and quantum mechanics on Riemann surfaces in an external magnetic field
description: scientific article; zbMATH DE number 589588