×

Geometric and quantum properties of charged particles in monochromatic electromagnetic knot background. (English) Zbl 1480.53028

Mladenov, Ivaïlo M. (ed.) et al., Proceedings of the 22nd international conference on geometry, integrability and quantization, Varna, Bulgaria, June 8–13, 2020. Sofia: Bulgarian Academy of Sciences, Institute of Biophysics and Biomedical Engineering. Geom. Integrability Quantization 22, 107-120 (2021).
In this paper, the authors review recent results on the interaction of the topological electromagnetic fields with matter, in particular with spinless and spin half charged particles obtained earlier. The problems discussed here are the generalized Finsler geometries and their dualities in the Trautman-Rañada backgrounds, the classical dynamics of the charged particles in the single non-null knot mode background and the quantization in the same background in the strong field approximation. The main results of this paper lie in Section 5, where the authors present the quantization of a spin particle in the same knot mode background discussed in Section 4. In the last section, they give a short list of interesting open problems about the systems discussed in the paper here.
For the entire collection see [Zbl 1468.53002].

MSC:

53B40 Local differential geometry of Finsler spaces and generalizations (areal metrics)
78A25 Electromagnetic theory (general)
53D50 Geometric quantization
53Z05 Applications of differential geometry to physics
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] Arrayás M., Bouwmeester D. and Trueba J., Knots in Electromagnetism, Phys. Rep. 667 (2017) 1-61. · Zbl 1359.78002
[2] Arrayás M. and Trueba J., Electromagnetic Torus Knots, J. Phys. A 48 (2015) 025203. · Zbl 1325.78005
[3] Arrayás M. and Trueba J., The Method of Fourier Transforms Applied to Electromag-netic Knots, European J. Phys. 40 (2019) 015205. · Zbl 1421.78003
[4] Berestetskii V., Lifshitz E. and Pitaevskii L., Quantum Electrodynamics, 2 nd Edn, Butterworth-Heinemann, Oxford 1982.
[5] Boca M., On the Properties of the Volkov Solutions of the Klein-Gordon Equation, J. Phys. A 44 (2011) 445303. · Zbl 1231.81026
[6] Brink L., Deser S., Zumino B., Di Vecchia P. and Howe P., Local Supersymmetry for Spinning Particles, Phys. Lett. B 64 (1976) 435-438. Erratum: Phys. Lett. B 68 (1977) 488.
[7] Brink L., Di Vecchia P. and Howe P., A Lagrangian Formulation of the Classical and Quantum Dynamics of Spinning Particles, Nucl. Phys. B 118 (1977) 76-94.
[8] Crişan A. and Vancea I., Nonlinear Dynamics of a Charged Particle in a Strong Non-Null Knot Wave Background, Int. J. Mod. Phys. A 35 (2020) 2050113.
[9] Crişan A. and Vancea I., Finsler Geometries from Topological Electromagnetism, Eur. Phys. J. C 80 (2020) 1-12.
[10] Mackenroth K., Quantum Radiation in Ultra-Intense Laser Pulses, Springer, Heidel-berg 2014.
[11] Rañada A., A Topological Theory of the Electromagnetic Field, Lett. Math. Phys. 18 (1989) 97-106. · Zbl 0687.57015
[12] Rañada A., Knotted Solutions of the Maxwell Equations in Vacuum, J. Phys. A 23 (1990) L815-L820.
[13] Rund H., The Differential Geometry of Finsler Spaces, Springer, Berlin 1959. · Zbl 0087.36604
[14] Trautman A., Solutions of the Maxwell and Yang-Mills Equations Associated with Hopf Fibrings, Int. J. Theor. Phys. 16 (1977) 561-565.
[15] Vacaru S., Spinors in Higher Dimensional and Locally Anisotropic Spaces, J. Math. Phys. 37 (1996) 508-523. · Zbl 0870.53054
[16] Vancea I., On the Existence of the Field Line Solutions of the Einstein-Maxwell Equa-tions, Int. J. Geom. Meth. Mod. Phys. 15 (2017) 1850054. · Zbl 1386.83042
[17] Vancea I., Knots and Maxwell’s Equations, In: Essential Guide to Maxwell’s Equa-tions, Ed. C. Erickson, Nova Science Publishers, Hauppauge 2018, pp 1-29.
[18] Vancea I., Field Line Solutions of the Einstein-Maxwell Equations, In: Essential Guide to Maxwell’s Equations, Ed. C. Erickson, Nova Science Publishers, Haup-pauge 2018, pp 30-56.
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.