Octonion massive electrodynamics

Research Article


In this paper, we have made an attempt to reformulate the generalized field equation and various quantum equations of massive dyons in terms of octonion eight dimensional space as the combination of two (external and internal) four dimensional spaces. The octonion forms of generalized potential and current equations of massive dyons are discussed in consistent manner. It has been shown that due to the non associativity of octonion variables it is necessary to impose certain constraints to describe generalized octonion massive electrodynamics in manifestly covariant and consistent manner.


Octonion Electrodynamics Dyons Massive dyons Generalized field equation Proca–Maxwell’s equations 



I am grateful to Professor OPS Negi, Professor PS Bisht and BCS Chauhan for inspiring discussions. I thank to referees for instructive comments on the manuscript.


  1. 1.
    Dickson, L.E.: On quaternions and their generalization and the history of the eight square theorem. Ann. Math. 20, 155 (1919)CrossRefMATHGoogle Scholar
  2. 2.
    Hamilton, W.R.: Elements of Quaternions. Chelsea Publications Co., New York (1969)Google Scholar
  3. 3.
    Tait, P.G.: An elementary Treatise on Quaternions. Oxford Univ. Press, New York (1875)Google Scholar
  4. 4.
    Finklestein, D., Jauch, J.M., Schiminovich, S., Speiser, D.: Principle of general quaternion covariance. J. Math. Phys. 4, 788 (1963)ADSCrossRefGoogle Scholar
  5. 5.
    Adler, S.L.: Quaternion Quantum Mechanics and Quantum Fields. Oxford Univ. Press, New York (1995)Google Scholar
  6. 6.
    Bisht, P.S., Negi, O.P.S., Rajput, B.S.: Quaternion Gauge theory of dyonic fields. Prog. Theor. Phys. 85, 157 (1991)ADSCrossRefGoogle Scholar
  7. 7.
    Majernik, V.: Quaternionic formulation of the classical fields. Adv. Cliff. Alg. 9, 119 (1999)CrossRefMATHMathSciNetGoogle Scholar
  8. 8.
    Kravchenkov, V.V.: Applied Quaternion Analysis. Helderman, Germany (2003)Google Scholar
  9. 9.
    Shalini, Bisht, Bisht, P.S., Negi, O.P.S.: Revisiting quaternion formulation and electromagnetism. Nuovo Cimento B 113, 1449 (1998)ADSGoogle Scholar
  10. 10.
    Morita, K.: Octonions quarks and QCD. Prog. Theor. Phys. 65, 787 (1981)ADSCrossRefGoogle Scholar
  11. 11.
    Graves, R.P.: Life of Sir William Rowan Hamilton, vol. 3. Arno Press, New York (1975)Google Scholar
  12. 12.
    Baez, J.C.: The octonions. Bull. Am. Math. Soc. 39, 145 (2001). math. RA/0105155CrossRefMathSciNetGoogle Scholar
  13. 13.
    Gunaydin, M., Gursey, F.: Quark statistics and octonions. Phys. Rev. D9, 3387 (1974)ADSGoogle Scholar
  14. 14.
    Gürsey, F.: Non-associative Algebras in Quantum Mechanics and Particle Physics. U. Virginia, Charlottesville (1977)Google Scholar
  15. 15.
    Lukierski, J., Toppan, F.: Generalized space-time supersymmetries, division algebras and octonionic M-theory. Phys. Lett. B 539, 266 (2002)ADSCrossRefMATHMathSciNetGoogle Scholar
  16. 16.
    Schray, J.: Octonions and Supersymmetry, Ph.D. thesis, Department of Physics, Oregon State University, Corvallis (1994)Google Scholar
  17. 17.
    Foot, R., Joshi, G.C.: Space-time symmetries of superstring and Jordan algebras. Int. J. Theor. Phys. 28, 1449 (1989)CrossRefMATHMathSciNetGoogle Scholar
  18. 18.
    Tolan, T., Özdas, K., Tansili, M.: Reformulation of electromagnetism with octonions. Nuovo Cimento B 121, 43 (2006)ADSGoogle Scholar
  19. 19.
    Bisht, P.S., Pandey, B., Negi, O.P.S.: Interpretations of octonion wave equations. FIZIKA B (Zagreb) 17, 405 (2008)ADSGoogle Scholar
  20. 20.
    Gamba, A.: Maxwell’s equations in octonion form. Nuovo Cimento 111A, 3 (1998)Google Scholar
  21. 21.
    Tanışlı, M., Kansu, M.E.: Octonionic Maxwell’s equations for bi-isotropic media. J. Math. Phys. 52, 053511 (2011)ADSCrossRefMathSciNetGoogle Scholar
  22. 22.
    Gogberashvili, M.: Octonionic electrodynamics. J. Phys. A: Math. Gen. 39, 7099 (2006)ADSCrossRefMATHMathSciNetGoogle Scholar
  23. 23.
    Nurowski, P.: Split octonions and Maxwell equations. Acta Phys. Pol. A 116, 992 (2009)Google Scholar
  24. 24.
    Chanyal, B.C., Bisht, P.S., Negi, O.P.S.: Generalized split-octonion electrodynamics. Int. J. Theor. Phys. 50, 1919 (2011)CrossRefMATHMathSciNetGoogle Scholar
  25. 25.
    Chanyal, B.C., Bisht, P.S., Negi, O.P.S.: Octonionic non-Abelian Gauge theory. Int. J. Theor. Phys. 52, 3522 (2013)CrossRefMATHGoogle Scholar
  26. 26.
    Pais, A.: Remark on the algebra of interactions. Phys. Rev. Lett. 7, 291 (1961)ADSCrossRefGoogle Scholar
  27. 27.
    Dirac, P.A.M.: Quantized singularities in the electromagnetic field. Proc. R. Soc. Lond. A 133, 60 (1931)ADSCrossRefGoogle Scholar
  28. 28.
    Dirac, P.A.M.: The theory of magnetic poles. Phy. Rev. 74, 817 (1948)ADSCrossRefMATHMathSciNetGoogle Scholar
  29. 29.
    Maxwell, J.C.: A Treatise on Electricity and Magnetism. Clarendon Press, Oxford (1873)Google Scholar
  30. 30.
    Panofsky, W., Phillips, M.: Classical Electricity and Magnetism. Addison-Wesley, Reading (1964)Google Scholar
  31. 31.
    Perlmutter, A.: New Pathways in High Energy Physics. Plenumm Press, New York (1976)CrossRefGoogle Scholar
  32. 32.
    Heaviside, O.: Electromagnetic Theory. Chelsa Pub. Comp, London (1893)Google Scholar
  33. 33.
    Rajput, B.S., Kumar, S., Negi, O.P.S.: Quaternionic formulation for generalized field equations in the presence of dyons. Lett. Nuovo Cimento 34, 180 (1982)CrossRefGoogle Scholar
  34. 34.
    Proca, A.: Sur 1’equation de Dirac. Compt. Rend. 190, 1377 (1930)MATHGoogle Scholar
  35. 35.
    Ignatiev, AYu., Joshi, G.C.: Massive electrodynamics and the magnetic monopoles. Phys. Rev. D 53, 984 (1996)ADSCrossRefMathSciNetGoogle Scholar
  36. 36.
    Bogomolny, E.B.: Stability of classical solutions. Sov. J. Nucl. Phys. 24, 449 (1976)Google Scholar
  37. 37.
    Chanyal, B.C., Bisht, P.S., Negi, O.P.S.: Octonion quantum chromodynamics. Int. J. Theor. Phys. 51, 3410 (2012)CrossRefMATHMathSciNetGoogle Scholar
  38. 38.
    Chanyal, B.C., Bisht, P.S., Negi, O.P.S.: Generalized octonion electrodynamics. Int. J. Theor. Phys. 49, 1333 (2010)CrossRefMATHMathSciNetGoogle Scholar
  39. 39.
    Bisht, P.S., Negi, O.P.S., Rajput, B.S.: Quaternion formulation for unified fields of dyons and gravito-dyons. Ind. J. Pure Appl. Math. 24, 543 (1993)MathSciNetGoogle Scholar
  40. 40.
    Tanisli, M., Jancewicz, B.: Octonionic Lorenz-like condition. Pramana. J. Phys. 78, 165 (2012)ADSCrossRefGoogle Scholar
  41. 41.
    Chanyal, B.C., Bisht, P.S., Negi, O.P.S.: Octonion representation of the superstring theory. Int. J. Eng. Res. Tech. 2, 1459 (2013)Google Scholar
  42. 42.
    Chanyal, B.C., Bisht, P.S., Negi, O.P.S.: Octonion and conservation laws for dyons. Int. J. Mod. Phys. A 28, 1350125 (2013)ADSCrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media New York 2013

Authors and Affiliations

  1. 1.Department of PhysicsKumaun UniversityAlmoraIndia

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