Semi-Classical Quantum Generalization of the London Equations and the Monopole Hypothesis

Authors: Aliev I.N., Samedova Z.A., Lyatifov R.E. Published: 24.08.2023
Published in issue: #4(109)/2023  
DOI: 10.18698/1812-3368-2023-4-39-51

Category: Physics | Chapter: Theoretical Physics  
Keywords: cooper pairs, monopole, dyon, Abrikosov vortex


The paper considers the London equation semi-classical generalization leading to a connection between the Cooper pairs magnetic flux quantization and the electric charge discreteness. Using the Bohr --- Sommerfeld quantization rule, a derivation of the magnetic flux quantization was made on the basis of the fluxoid uniqueness. The resulting quantization was applied to the magnetic monopoles hypothesis proposed by Dirac, which remains relevant due to the asymmetry present in the modern physics in describing electrical and magnetic properties of matter. On a fairly simple model of the possible experiment, an option of registering a monopole by a jump in the magnetic induction flux and the associated alteration in the circuit current were studied. The paper analyzed the problems of the monopole different measurement units and the results similar to those obtained on the basis of the Schwinger series of works, where he proceeded from considering introduction of a hypothetical particle with the electric and magnetic charges, i.e., the dyon. Possible explanation of the Abrikosov vortex is presented, it is based on vortex representation in the form of a magnetized thin thread through the magnetic tubes, at the ends of which monopoles of different charges (dipole) are positioned. Unlike most the works devoted to this problem, calculations were performed in the SI system. The monopole quantization conditions were derived

Please cite this article in English as:

Aliev I.N., Samedova Z.A., Lyatifov R.E. Semi-classical quantum generalization of the London equations and the monopole hypothesis. Herald of the Bauman Moscow State Technical University, Series Natural Sciences, 2023, no. 4 (109), pp. 39--51 (in Russ.). DOI: https://doi.org/10.18698/1812-3368-2023-4-39-51


[1] Tolmachev V.V. Kvaziklassicheskoe priblizhenie v kvantovoy mekhanike [Quasiclassical approximation in quantum mechanics]. Moscow, MSU Publ., 1980.

[2] Migdal A.B., Kraynov V.P. Priblizhennye metody kvantovoy mekhaniki [Approximated methods of quantum mechanics]. Moscow, Nauka Publ., 1966.

[3] Shmidt V.V. Vvedenie v fiziku sverkhprovodnikov [Introduction in physics of superconductors]. Moscow, MTsNMO Publ., 2000.

[4] Aliev I.N., Melikyants D.G. On potentials in Londons’ electrodynamics. Herald of the Bauman Moscow State Technical University, Series Natural Sciences, 2016, no. 2 (65), pp. 42--50 (in Russ.). DOI: http://dx.doi.org/10.18698/1812-3368-2016-2-42-50

[5] Zhernovoy A.I. Quantization of magnetic flow created by nanoparticle of magnetite. Nauchnoe priborostroenie, 2018, vol. 28, no. 2, pp. 45--48 (in Russ.).

[6] Bolotovskiy B.M., Usachev Yu.D. (eds). Monopol Diraka. Sb. statey [Dirac’s Monopoly. Collection of articles]. Moscow, Mir Publ., 1970.

[7] Coleman S. The magnetic monopole fifty years later. UFN, 1984, vol. 144, no. 2, pp. 277--340 (in Russ.). DOI: https://doi.org/10.3367/UFNr.0144.198410d.0277

[8] Dolgov A.D. The magnetic monopole after its jubilee. Sov. Phys. Usp., 1984, vol. 27, no. 10, pp. 786--789. DOI: https://doi.org/10.1070/PU1984v027n10ABEH004137

[9] Vandewalle N., Dorbolo S. Magnetic ghosts and monopoles. New J. Phys., 2014, vol. 16, no. 1, art. 013050. DOI: https://doi.org/10.1088/1367-2630/16/1/013050

[10] Dirac P.A.M. Pretty mathematics. Int. J. Theor. Phys., 1982, vol. 21, no. 8-9, pp. 603--605. DOI: https://doi.org/10.1007/BF02650229

[11] Aliev I.N. Termodinamika i elektrodinamika sploshnykh sred [Thermodynamics and electrodynamics of continuous medium]. Moscow, BMSTU Publ., 2018.

[12] Aliev I.N., Kopylov I.S. Use of Dirac monopoles formalism in some magnetism problems. Herald of the Bauman Moscow State Technical University, Series Natural Sciences, 2015, no. 6 (63), pp. 25--39 (in Russ.). DOI: http://dx.doi.org/10.18698/1812-3368-2015-6-25-39

[13] Panat P.V. A new derivation of Dirac’s magnetic monopole strength. Eur. J. Phys., 2003, vol. 24, no. 2, pp. 111--114. DOI: http://dx.doi.org/10.1088/0143-0807/24/2/351

[14] Samedova Z.A. Variatsionnyy metod v magnitoelektrodinamike khorosho provodyashchikh sploshnykh sred. Avtoref. dis. kand. fiz.-mat. nauk [The variational method in the magnetoelectrodynamics of well-conducting continuum media. Abs. Cand. Sc. (Phys.-Math.) Diss.]. Moscow, BMSTU, 2022 (in Russ.).

[15] Schwinger J. Electric- and magnetic-charge renormalization. I. Phys. Rev., 1966, vol. 151, iss. 4, pp. 1048--1054. DOI: https://doi.org/10.1103/PhysRev.151.1048

[16] Schwinger J. Magnetic charge and quantum field theory. Phys. Rev., 1966, vol. 144, iss. 4, pp. 1087--1093. DOI: https://doi.org/10.1103/PhysRev.144.1087

[17] Schwinger J. Sources and magnetic charge. Phys. Rev., 1968, vol. 173, iss. 5, pp. 1536--1544. DOI: https://doi.org/10.1103/PhysRev.173.1536

[18] Schwinger J. A magnetic model of matter: a speculation probes deep within the structure of nuclear particles and predicts a new form of matter. Science, 1969, vol. 165, no. 3895, pp. 757--761.DOI: https://doi.org/10.1126/science.165.3895.757

[19] Gomberoff L., Tolmachev V. Is parity violated in weak interaction? Nuov. Cim. A, 1971, vol. 3, no. 3, pp. 657--662. DOI: https://doi.org/10.1007/BF02813566

[20] de Liano M., Tolmachev V.V. Multiple phases in a new statistical boson--fermion model of superconductivity. Physica A, 2003, vol. 317, iss. 3-4, pp. 546--564. DOI: https://doi.org/10.1016/S0378-4371(02)01348-1

[21] Milton K.A. Theoretical and experimental status of magnetic monopoles. Rep. Prog. Phys., 2006, vol. 69, no. 6, pp. 1637--1711. DOI: http://dx.doi.org/10.1088/0034-4885/69/6/R02

[22] Essmann U., Trauble H. The direct observation of individual flux lines in type II superconductors. Phys. Lett. A, 1967, vol. 24, iss. 10, pp. 526--527. DOI: https://doi.org/10.1016/0375-9601(67)90819-5