Geodesic
Geometry and quasiclassical quantization of magnetic monopoles
Teoretičeskaâ i matematičeskaâ fizika, Tome 218 (2024) no. 1, pp. 149-167 Cet article a éte moissonné depuis la source Math-Net.Ru

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We present the basic physical and mathematical ideas (P. Curie, Darboux, Poincaré, Dirac) that led to the concept of magnetic charge, the general construction of magnetic Laplacians for magnetic monopoles on Riemannian manifolds, and the results of Kordyukov and the author on the quasiclassical approximation for eigensections of these operators.
Mots-clés : quasiclassical approximation
Keywords: magnetic Laplacian, magnetic monopole. 
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I. A. Taimanov. Geometry and quasiclassical quantization of magnetic monopoles. Teoretičeskaâ i matematičeskaâ fizika, Tome 218 (2024) no. 1, pp. 149-167. http://geodesic.mathdoc.fr/item/TMF_2024_218_1_a8/

[1] Yu. A. Kordyukov, I. A. Taimanov, “Kvaziklassicheskoe priblizhenie dlya magnitnykh monopolei”, UMN, 75:6(456) (2020), 85–106 | DOI | DOI | MR | Zbl

[2] Yu. A. Kordyukov, I. A. Taimanov, “Formula sleda dlya magnitnogo laplasiana”, UMN, 74:2(446) (2019), 149–186 | DOI | DOI | MR | Zbl

[3] Y. A. Kordyukov, I. A. Taimanov, “Trace formula for the magnetic Laplacian on a compact hyperbolic surface”, Regul. Chaotic Dyn., 27:4 (2022), 460–476 | DOI | MR

[4] Ya. M. Shnir, Magnetic Monopoles, Theoretical and Mathematical Physics, Springer, Berlin, 2005 | DOI | MR

[5] P. Curie, “Sur la possibilité d'existence de la conductibilité magnétique et du magnétisme libre”, J. Phys. Theor. Appl., 3:1 (1894), 415–417 | DOI

[6] H. Poincaré, “Remarques sur une expérience de M. Birkeland”, C. R. Acad. Sci., 123 (1896), 530–533

[7] G. Darboux, “Problème de mécanique”, Bulletin des Sciences Mathématiques et Astronomiques, Serie 2, 2:1 (1878), 433–436

[8] J. J. Thomson, “Cathode rays”, Philos. Mag., 44:269 (1897), 293–316 | DOI

[9] P. A. M. Dirak, “Kvantovannye singulyarnosti v elektromagnitnom pole”, Sobranie nauchnykh trudov, v. II, Kvantovaya teoriya (nauchnye stati 1924–1947 gg.), Fizmatlit, M., 2003, 388–398 | DOI | Zbl

[10] I. E. Tamm, “Obobschennye sharovye funktsii i volnovye funktsii elektrona v pole magnitnogo polyusa”, Sobranie nauchnykh trudov, Nauka, M., 1975, 186–195 | DOI | Zbl

[11] P. A. M. Dirak, “Kontseptsiya monopolya”, Sobranie nauchnykh trudov, v. III, Kvantovaya teoriya (nauchnye stati 1948–1984 gg.), Fizmatlit, M., 2004, 189–200 | DOI | MR

[12] T. T. Wu, C. N. Yang, “Concept of nonintegrable phase factors and global formulation of gauge fields”, Phys. Rev. D, 12:12 (1975), 3845–3857 | DOI | MR

[13] T. T. Wu, C. N. Yang, “Dirac monopole without strings: monopole harmonics”, Nucl. Phys. B, 107:3 (1976), 365–380 | DOI | MR

[14] V. P. Maslov, Teoriya vozmuschenii i asimptoticheskie metody, Izd-vo Mosk. un-ta, M., 1965 | Zbl

[15] V. P. Maslov, M. V. Fedoryuk, Kvaziklassicheskoe priblizhenie dlya uravnenii kvantovoi mekhaniki, Nauka, M., 1976 | MR | MR

[16] S. P. Novikov, “Gamiltonov formalizm i mnogoznachnyi analog teorii Morsa”, UMN, 37:5(227) (1982), 3–49 | DOI | MR | Zbl

[17] Yu. A. Kordyukov, I. A. Taimanov, “Kvaziklassicheskoe priblizhenie monopolnykh garmonik”, Matem. zametki, 114:6 (2023), 848–862 | DOI

[18] M. V. Karasev, V. P. Maslov, Nelineinye skobki Puassona. Geometriya i kvantovanie, Nauka, M., 1991 | MR

[19] I. Bryuning, R. V. Nekrasov, A. I. Shafarevich, “Kvantovanie periodicheskikh dvizhenii na kompaktnykh poverkhnostyakh postoyannoi otritsatelnoi krivizny v magnitnom pole”, Matem. zametki, 81:1 (2007), 32–42 | DOI | DOI | MR | Zbl