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Sedeonic Field Equations for Dyons

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Abstract

We discuss the theoretical description of dyons having simultaneously both electric and magnetic charges on the basis of space-time algebra of 16-component sedeons. We show that the generalized sedeonic equations for electromagnetic field of dyons can be reformulated in equivalent canonical form as the equations for redefined field potentials, field strengths and sources. The relations for energy and momentum as well as the relations for Lorentz invariants of dyonic electromagnetic field are derived. Additionally, we discuss the sedeonic second-order and first-order wave equations describing the quantum behavior of dyons in an external dyonic electromagnetic field.

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References

  1. Bisht, P.S., Negi, O.P.S., Rajput, B.S.: Quaternion gauge theory of dyonic fields. Progr. Theor. Phys. 85, 157 (1991)

    Article  ADS  Google Scholar 

  2. Bisht, P.S., Dangwal, S., Negi, O.P.S.: Unified split octonion formulation of dyons. Int. J. Theor. Phys. 47, 2297 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  3. Chanyal, B.C.: Generalized Klein–Gordon field equations with octonion space-time (OST) algebra. Chin. J. Phys. 55(2), 432–443 (2017)

    Article  Google Scholar 

  4. Chanyal, B.C.: A relativistic quantum theory of dyons wave propagation. Can. J. Phys. 95(12), 1200–1207 (2017)

    Article  ADS  Google Scholar 

  5. Chanyal, B.C., Bisht, P.S., Negi, O.P.S.: Generalized octonion electrodynamics. Int. J. Theor. Phys. 49(6), 1333 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  6. Chanyal, B.C., Bisht, P.S., Negi, O.P.S.: Octonion and conservation laws for dyons. Int. J. Mod. Phys. A 28, 1350125 (2013)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  7. Chanyal, B.C., Chanyal, S.K., Singh, V., Rawat, A.S.: Proca–Maxwell equations for dyons with quaternion. Appl. Math. Phys. 4(1), 9–15 (2016)

    Google Scholar 

  8. Coceal, O., Sabra, W.A., Thomas, S.: Duality-invariant magnetohydrodynamics and dyons. Europhys. Lett. 35(4), 277–282 (1996)

    Article  ADS  Google Scholar 

  9. Dehnen, H., Negi, O.P.S.: Electromagnetic duality, quaternion and supersymmetric gauge theories of dyons. Int. J. Theor. Phys. 50, 19081918 (2011)

    Google Scholar 

  10. Demir, S., Özdaş, K.: Dual quaternionic reformulation of classical electromagnetism. Acta Phys. Slov. 53(6), 429–436 (2003)

    Google Scholar 

  11. Demir, S., Tanışlı, M.: Sedenionic formulation for generalized fields of dyons. Int. J. Theor. Phys. 51(4), 1239–1252 (2012)

    Article  MATH  Google Scholar 

  12. Demir, S., Tanışlı, M., Candemir, N.: Hyperbolic quaternion formulation of electromagnetism. Adv. Appl. Clifford Algebras 20(3–4), 547–563 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  13. Demir, S., Tanışlı, M., Kansu, M.E.: Generalized hyperbolic octonion formulation for the fields of massive dyons and gravito-dyons. Int. J. Theor. Phys. 52, 3696–3711 (2013)

    Article  MATH  Google Scholar 

  14. Dirac, P.A.M.: Quantised singularities in the electromagnetic field. Proc. R. Soc. Lond. Ser. A 133, 60–72 (1931)

    Article  ADS  MATH  Google Scholar 

  15. Dirac, P.A.M.: The theory of magnetic poles. Phys. Rev. 74, 817 (1948)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  16. Dirac, P.A.M.: The Principles of Quantum Mechanics. Clarendon Press, Oxford (1958)

    MATH  Google Scholar 

  17. Gamba, A.: Maxwells equations in octonion form. Nuovo Cimento A 111(3), 293–302 (1998)

    ADS  Google Scholar 

  18. Goddard, P., Olive, D.I.: Magnetic monopoles in gauge field theories. Rep. Progr. Phys. 41, 1357–1437 (1978)

    Article  ADS  Google Scholar 

  19. Grudsky, S.M., Khmelnytskaya, K.V., Kravchenko, V.V.: On a quaternionic Maxwell equation for the time-dependent electromagnetic field in a chiral medium. J. Phys. A Math. Gen. 37, 4641–4647 (2004)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  20. Imaeda, K.: A new formulation of classical electrodynamics. Nuovo cimento 32(1), 138–162 (1976)

    Article  MathSciNet  Google Scholar 

  21. Kravchenko, V.G., Kravchenko, V.V.: Quaternionic factorization of the Schrdinger operator and its applications to some first order systems of mathematical physics. J. Phys. A 36(44), 11285–11297 (2003)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  22. Macfarlane, A.: Hyperbolic quaternions. In: Proceedings of the Royal Society at Edinburgh, 1899–1900 Sessions, pp. 169–181 (1902)

  23. Majernik, V.: Quaternionic formulation of the classical fields. Adv. Appl. Clifford Algebras 9(1), 119–130 (1999)

    Article  MathSciNet  MATH  Google Scholar 

  24. Mironov, V.L., Mironov, S.V.: Octonic second-order equations of relativistic quantum mechanics. J. Math. Phys. 50(012302), 1–13 (2009)

    MathSciNet  MATH  Google Scholar 

  25. Mironov, V.L., Mironov, S.V.: Sedeonic generalization of relativistic quantum mechanics. Int. J. Mod. Phys. A 24(32), 6237–6254 (2009)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  26. Mironov, V.L., Mironov, S.V.: Reformulation of relativistic quantum mechanics equations with non-commutative sedeons. Appl. Math. 4(10C), 53–60 (2013)

    Article  Google Scholar 

  27. Mironov, V.L., Mironov, S.V.: Sedeonic equations of gravitoelectromagnetism. J. Mod. Phys. 5(10), 917–927 (2014)

    Article  Google Scholar 

  28. Mironov, S.V., Mironov, V.L.: Sedeonic equations of massive fields. Int. J. Theor. Phys. 54(1), 153–168 (2015)

    Article  MathSciNet  MATH  Google Scholar 

  29. Mironov, V.L., Mironov, S.V.: Gauge invariance of sedeonic equations for massive and massless fields. Int. J. Theor. Phys. 55(7), 3105–3119 (2016)

    Article  MathSciNet  MATH  Google Scholar 

  30. Mironov, V.L., Mironov, S.V.: Two types of Lorentz transformations for massless fields. J. Geom. Symmetry Phys. 44, 83–96 (2017)

    Article  MathSciNet  MATH  Google Scholar 

  31. Schwinger, J.: A magnetic model of matter. Science 165(3895), 757761 (1969)

    Article  Google Scholar 

  32. Tanışlı, M., Kansu, M.E., Demir, S.: Reformulation of electromagnetic and gravito-electromagnetic equations for Lorentz system with octonion algebra. Gen. Relativ. Gravit. 46, 1739 (2014)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  33. Tolan, T., Özdaş, K., Tanışlı, M.: Reformulation of electromagnetism with octonions. Nuovo Cimento B 121(1), 43–55 (2006)

    ADS  MathSciNet  Google Scholar 

  34. Ulrych, S.: Considerations on the hyperbolic complex Klein–Gordon equation. J. Math. Phys. 51(6), 063510 (2010)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  35. Ulrych, S.: Higher spin quaternion waves in the Klein–Gordon theory. Int. J. Theor. Phys. 52(1), 279 (2013)

    Article  MathSciNet  MATH  Google Scholar 

  36. Weng, Z.-H.: Forces in the complex octonion space. Int. J. Geom. Methods Mod. Phys. 13, 1650076 (2016)

    Article  MathSciNet  MATH  Google Scholar 

  37. Weng, Z.-H.: Physical quantities and spatial parameters in the complex octonion curved space. Gen. Relativ. Gravit. 48(12), 153 (2016)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  38. Weng, Z.-H.: Spin angular momentum of proton spin puzzle in complex octonion spaces. Int. J. Geom. Methods Mod. Phys. 14(7), 1750102 (2017)

    Article  MathSciNet  MATH  Google Scholar 

  39. Weng, Z.-H.: Color confinement and spatial dimensions in the complex-sedenion space. Adv. Math. Phys. 2017, 9876464 (2017)

    Article  MathSciNet  Google Scholar 

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Acknowledgements

The authors are very thankful to Galina Mironova for the assistance and moral support. Special thanks to Prof. Murat Tanişli (Anadolu University, Eskişehir, Turkey) for the stimulating discussion on this topic. We also thank the reviewers for their valuable comments.

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Correspondence to Victor L. Mironov.

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Communicated by Vladislav Kravchenko.

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Mironov, V.L., Mironov, S.V. Sedeonic Field Equations for Dyons. Adv. Appl. Clifford Algebras 28, 64 (2018). https://doi.org/10.1007/s00006-018-0886-3

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