This article is cited in 2 papers

Monopole solutions as three-dimensional generalizations of Kronecker series

K. M. Bulycheva<sup>ab

a</sup> Moscow Physico-Technical Institute, Dolgoprudny, Moscow Oblast, Russia
^b Institute for Theoretical and Experimental Physics, Moscow, Russia

Abstract: We investigate the Dirac monopole on a three-dimensional torus as a solution of the Bogomolny equations with nontrivial boundary conditions. We show that a suitable analytic continuation of the obtained solution is a three-dimensional generalization of the Kronecker series, satisfies the corresponding functional equation, and is invariant under modular transformations.

Keywords: Bogomolny equation, monopole, Kronecker series, modular invariance.

Received: 24.11.2011
Revised: 23.01.2012

DOI: 10.4213/tmf6949

 English version: Theoretical and Mathematical Physics, 2012, 172:3, 1232–1242

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