Geodesic
Monopole solutions as three-dimensional generalizations of Kronecker
Teoretičeskaâ i matematičeskaâ fizika, Tome 172 (2012) no. 3, pp. 403-414 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

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.
Mots-clés : Bogomolny equation, monopole
Keywords: Kronecker series, modular invariance. 
@article{TMF_2012_172_3_a5,
     author = {K. M. Bulycheva},
     title = {Monopole solutions as three-dimensional generalizations of {Kronecker}},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {403--414},
     year = {2012},
     volume = {172},
     number = {3},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_2012_172_3_a5/}
}
TY  - JOUR
AU  - K. M. Bulycheva
TI  - Monopole solutions as three-dimensional generalizations of Kronecker
JO  - Teoretičeskaâ i matematičeskaâ fizika
PY  - 2012
SP  - 403
EP  - 414
VL  - 172
IS  - 3
UR  - http://geodesic.mathdoc.fr/item/TMF_2012_172_3_a5/
LA  - ru
ID  - TMF_2012_172_3_a5
ER  - 
%0 Journal Article
%A K. M. Bulycheva
%T Monopole solutions as three-dimensional generalizations of Kronecker
%J Teoretičeskaâ i matematičeskaâ fizika
%D 2012
%P 403-414
%V 172
%N 3
%U http://geodesic.mathdoc.fr/item/TMF_2012_172_3_a5/
%G ru
%F TMF_2012_172_3_a5
K. M. Bulycheva. Monopole solutions as three-dimensional generalizations of Kronecker. Teoretičeskaâ i matematičeskaâ fizika, Tome 172 (2012) no. 3, pp. 403-414. http://geodesic.mathdoc.fr/item/TMF_2012_172_3_a5/

[1] P. A. M. Dirac, Phys. Rev., 74 (1948), 817–830 | DOI | MR | Zbl

[2] P. A. M. Dirac, Proc. R. Soc. Lond. A, 133:821 (1931), 60–71 | DOI | Zbl

[3] P. Kronheimer, ALE gravitational instantons, D. Phil. thesis, Oxford Univ., Oxford, 1986 (unpublished); S. K. Donaldson, P. B. Kronheimer, The Geometry of Four-manifolds, Oxford Univ. Press, Oxford, 1990 | MR | Zbl

[4] M. Atiyah, N. Hitchin, The Geometry and Dynamics of Magnetic Monopoles, Princeton Univ. Press, Princeton, NJ, 1988 | MR | Zbl

[5] M. I. Monastyrskii, A. G. Sergeev (red.), Monopoli: topologicheskie i variatsionnye metody, Sb. statei, Mir, M., 1989

[6] V. Rubakov, Classical Theory of Gauge Fields, Princeton Univ. Press, Princeton, NJ, 2002 | MR | Zbl

[7] Y. M. Shnir, Magnetic Monopoles, Texts and Monographs in Physics, Springer, Berlin, 2005 | MR | Zbl

[8] E. B. Bogomolnyi, YaF, 24:4 (1976), 861–870 | MR

[9] A. Kapustin, E. Witten, Commun. Number Theory Phys., 1:1 (2007), 1–236, arXiv: hep-th/0604151 | DOI | MR | Zbl

[10] A. M. Levin, M. A. Olshanetsky, A. V. Zotov, SIGMA, 5 (2009), 065, 22 pp., arXiv: 0811.3056 | DOI | MR | Zbl

[11] A. M. Levin, M. A. Olshanetsky, A. V. Smirnov, A. V. Zotov, Characteristic classes and integrable systems. General construction, arXiv: 1006.0702

[12] N. Hitchin, Duke Math. J., 54:1 (1987), 91–114 | DOI | MR | Zbl

[13] A. M. Levin, M. A. Olshanetsky, A. V. Zotov, Comm. Math. Phys., 236:1 (2003), 93–133, arXiv: nlin/0110045 | DOI | MR | Zbl

[14] A. M. Levin, M. A. Olshanetsky, A. V. Zotov, Comm. Math. Phys., 268:1 (2006), 67–103, arXiv: math/0508058 | DOI | MR | Zbl

[15] W. Nahm, Phys. Lett. B, 90:4 (1980), 413–414 ; E. Corrigan, P. Goddard, Ann. Phys., 154:1 (1984), 253–279 | DOI | MR | DOI | MR | Zbl

[16] R. Ward, “Integrable systems and twistors”, Integrable Systems (Oxford, September 14–19, 1997), Oxford Graduate Texts in Mathematics, 4, Oxford Univ. Press, Oxford, 1999, 121–134 | MR

[17] A. Weyl, Elliptic Functions According to Eisenstein and Kronecker, Ergebnisse der Mathematik und ihrer Grenzgebiete, 88, Springer, Berlin, New York, 1976 | MR

[18] H. S. M. Coxeter, W. O. J. Moser, Generators and Relations for Discrete Groups, Ergebnisse der Mathematik und ihrer Grenzgebiete, 14, Springer, Berlin, Heidelberg, New York, 1972 | MR | Zbl