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On the Internal Geometry of Trajectories of Charged Particles in Symmetric External Fields

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Russian Physics Journal Aims and scope

The curvature and torsion of trajectories of charges in external gauge fields, including fields of magnetic monopoles, have been determined. It has been shown that these quantities are effectively calculated with the help of the equations of motion and first integrals. For a wide class of magnetic fields, their form-invariant combination has been revealed.

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References

  1. B. A. Dubrovin, S. P. Novikov, and A. T. Fomenko, Modern Geometry [in Russian], Nauka, Moscow (1979).

    Google Scholar 

  2. B. M. Budak and S. V. Fomin, Multiple Integrals and Series [in Russian], Nauka, Moscow (1967).

    Google Scholar 

  3. L. D. Landau and E. M. Lifshitz, Mechanics, Butterworth-Heinemann, London (1976).

    MATH  Google Scholar 

  4. L. D. Landau and E. M. Lifshitz, The Classical Theory of Fields, Butterworth-Heinemann, London (1975).

    MATH  Google Scholar 

  5. D. V. Gal’tsov, Yu. V. Grats, and V. Ch. Zhukovskii, Classical Fields [in Russian], Moscow State University Publishing House, Moscow (1991).

    Google Scholar 

  6. Ya. M. Shnir, Magnetic Monopoles, Springer Verlag, Berlin (2005).

  7. P. A. M. Dirac, Proc. Roy. Soc. A, 133, 60 (1931).

    ADS  Google Scholar 

  8. J. Schwinger, Phys. Rev., 144, No. 4, 1087 (1966).

    Article  ADS  MathSciNet  Google Scholar 

  9. D. G. Boulware et al., Phys. Rev. D, 14, No. 10, 2708 (1976).

    Article  ADS  MathSciNet  Google Scholar 

  10. S. K. Wong, Nuouo Cimento A, 65, No. 4, 689 (1970).

    Article  ADS  Google Scholar 

  11. A. W. Wipf, J. Phys. A: Math. Gen., 18, 2379 (1985).

    Article  ADS  MathSciNet  Google Scholar 

  12. L. Feher, J. Phys. A: Math. Gen., 19, 1259 (1986).

    Article  ADS  Google Scholar 

  13. V. G. Bagrov and A. S. Vshivtsev, Motion of a Non-Abelian Particle in Color Fields, Preprint No. 14, Tomsk Affiliate of the Siberian Branch of the Academy of Sciences of the USSR (1987).

  14. M. I. Monastyrskii and A. M. Perelomov, Pis’ma Zh. Eksp. Teor. Fiz., 21, 94 (1975).

    Google Scholar 

  15. A. S. Shvarts, Quantum Theory and Topology [in Russian], Nauka, Moscow (1989).

    MATH  Google Scholar 

  16. P. Goddard and D. Olive, Rep. Prog. Phys., 41, 1357 (1978).

    Article  ADS  Google Scholar 

  17. A. W. Wipf, Helv. Phys. Acta, 58, 531 (1985).

    MathSciNet  Google Scholar 

  18. S. É. Korenblit and Kieun Lee, Russ. Phys. J., 53, No. 3, 302 (2010).

    Article  Google Scholar 

  19. A. I. Breev and A. A. Magazev, Russ. Phys. J., 59, No. 12, 2048 (2016).

    Article  Google Scholar 

  20. M. E. Peskin and D. V. Shreder, Introduction to Quantum Field Theory [in Russian], R & C Dynamics, Izhevsk (2001).

    Google Scholar 

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Correspondence to E. A. Voronova.

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Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 1, pp. 35–42, January, 2021.

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Voronova, E.A., Korenblit, S.É. On the Internal Geometry of Trajectories of Charged Particles in Symmetric External Fields. Russ Phys J 64, 39–49 (2021). https://doi.org/10.1007/s11182-021-02298-2

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  • DOI: https://doi.org/10.1007/s11182-021-02298-2

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