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Integrable generalisations of Dirac magnetic monopole

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journal contribution
posted on 24.11.2020, 15:28 by Alexander VeselovAlexander Veselov, Y Ye
We classify certain integrable (both classical and quantum) generalisations of Dirac magnetic monopole on topological sphere S2 with constant magnetic field, completing the previous local results by Ferapontov, Sayles and Veselov. We show that there are two integrable families of such generalisations with integrals, which are quadratic in momenta. The first family corresponds to the classical Clebsch systems, which can be interpreted as Dirac magnetic monopole in harmonic electric field. The second family is new and can be written in terms of elliptic functions on sphere S2 with very special metrics.

Funding

the Russian Science Foundation Grant No. 20-11-20214

History

School

  • Science

Department

  • Mathematical Sciences

Published in

Journal of Physics A: Mathematical and Theoretical

Volume

53

Issue

49

Publisher

IOP Publishing

Version

VoR (Version of Record)

Rights holder

© The authors

Publisher statement

This is an Open Access Article. It is published by IOP under the Creative Commons Attribution 4.0 Unported Licence (CC BY). Full details of this licence are available at: http://creativecommons.org/licenses/by/4.0/

Acceptance date

09/10/2020

Publication date

2020-11-17

Copyright date

2020

ISSN

1751-8113

eISSN

1751-8121

Language

en

Depositor

Prof Alexander Veselov. Deposit date: 24 November 2020

Article number

494004