Nontrivial \(U(1)\) bundles over tori and properties of many-particle systems with topological charge
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.
scientific article; zbMATH DE number 589588