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Generalized Gravi—Electromagnetism

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Abstract

A self consistant and manifestly covariant theory for the dynamics of four charges (masses) (namely electric, magnetic, gravitational, Heavisidian) has been developed in simple, compact and consistent manner. Starting with an invariant Lagrangian density and its quaternionic representation, we have obtained the consistent field equation for the dynamics of four charges. It has been shown that the present reformulation reproduces the dynamics of individual charges (masses) in the absence of other charge (masses) as well as the generalized theory of dyons (gravito-dyons) in the absence gravito-dyons (dyons).

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References

  1. Dirac, P.A.M.: Proc. R. Soc. Lond. A 133, 60 (1931)

    Article  MATH  ADS  Google Scholar 

  2. Dirac, P.A.M.: Phys. Rev. 74, 817 (1948)

    Article  MATH  MathSciNet  ADS  Google Scholar 

  3. ’t Hooft, G.: Nucl. Phys. B 79, 276 (1974)

    Article  MathSciNet  ADS  Google Scholar 

  4. Polyakov, A.M.: JETP Lett. 20, 194 (1974)

    ADS  Google Scholar 

  5. Julia, B., Zee, A.: Phys. Rev. D 11, 2227 (1975)

    Article  ADS  Google Scholar 

  6. Rajput, B.S., Joshi, D.C.: Hadron. J. 4, 1805 (1981)

    Google Scholar 

  7. Rajput, B.S., Joshi, D.C.: Pramana (India) 15, 153 (1980)

    Article  ADS  Google Scholar 

  8. Rajput, B.S., Prakash, O.: Indian J. Phys. A 53, 274 (1979)

    Google Scholar 

  9. Bisht, P.S., Negi, O.P.S., Rajput, B.S.: IL Nuovo Cimento A 104, 337 (1991)

    Article  ADS  Google Scholar 

  10. Bisht, P.S., Negi, O.P.S., Rajput, B.S.: Prog. Theor. Phys. 85, 157 (1991)

    Article  ADS  Google Scholar 

  11. Bisht, P.S., Negi, O.P.S., Rajput, B.S.: Int. J. Theor. Phys. 32, 2099 (1993)

    Article  MathSciNet  Google Scholar 

  12. Hamilton, W.R.: On a new species of imaginary quantities connected with a theory of quaternions. In: Proc. Royal Irish Academy vol. 2, pp. 424–434 (1843)

  13. Hamilton, W.R.: Elements of Quaternions, vols. I and II (First edition 1866; Second edition edited and expanded by C.J. Joly 1899–1901; Reprinted by Chelsea Publishing, New York, 1969) 1185 pp.

  14. Tait, P.G.: An Elementary Treatise on Quaternions. Clarendon, Oxford (1867)

    Google Scholar 

  15. Tait, P.G.: Scientific Papers. Cambridge University Press, Cambridge (1898), 2 volumes

    MATH  Google Scholar 

  16. Gsponer, A., Hurni, J.P.: Quaternion in mathematical physics (1): Alphabetical bibliography. Report ISRI0504 (4 March 2006) 100 pp. eprint arXiv:mathph/0510059

  17. Gsponer, A., Hurni, J.P.: Quaternion in mathematical physics (2): Analytical bibliography. Report ISRI0505 (4 March 2006) 113 pp. eprint arXiv:mathph/0511092

  18. Gsponer, A., Hurni, J.P.: Quaternion in mathematical physics (3): Notations and terminology. Report ISRI0506

  19. Gsponer, A., Hurni, J.P.: Quaternion in mathematical physics (4): Formulas and identities. Report ISRI0507

  20. Maxwell, J.C.: A dynamical theory of the electromagnetic field. R. Soc. Trans. 155, 459 (1865)

    Article  Google Scholar 

  21. Maxwell, J.C.: Address to the mathematical and physical sections of the British association. Brit. Ass. Rep. XL, 215–229 (1870)

    Google Scholar 

  22. Maxwell, J.C.: A Treatise on Electricity & Magnetism, vols. I, II. Dover, New York (1873)

    Google Scholar 

  23. Silberstein, L.: Ann. Phys. 22, 579 (1907)

    Article  Google Scholar 

  24. Silberstein, L.: Ann. Phys. 22, 783 (1907)

    Article  Google Scholar 

  25. Silberstein, L.: Philos. Mag. 23, 790 (1912)

    Google Scholar 

  26. Silberstein, L.: Philos. Mag. 25, 135 (1913)

    Google Scholar 

  27. Silberstein, L.: In: The Theory of Relativity, p. 135. MacMillan, London (1914), 295 pp.

    Google Scholar 

  28. Gürsey, F.: Applications of quaternions to field equations. Ph.D. thesis (unpublished), University of London (1950)

  29. Bork, A.M.: Vectors versus quaternions—the letters of nature. Am. J. Phys. 34, 202 (1966)

    Article  MATH  ADS  Google Scholar 

  30. Lanczos, C.: The relations of the homogeneous Maxwell’s equations to the theory of functions—a contribution to the theory of relativity and electrons. Verlagsbuchhandlung Josef Nemeth, Budapest (1919). Typeseted by Jean Pierre Hurni with a preface by Andre Gsponer (2004). eprint arXiv:physics/0408079

    Google Scholar 

  31. Lanczos, C.: William Rowan Hamilton—an appreciation. Am. Sci. 2, 129 (1967)

    Google Scholar 

  32. Edmonds, J.D. Jr.: Am. J. Phys. 22, 220 (1974)

    Article  ADS  Google Scholar 

  33. Edmonds, J.D. Jr.: Am. J. Phys. 46, 430 (1978)

    Article  MathSciNet  ADS  Google Scholar 

  34. Edmonds, J.D. Jr.: Adv. Appl. Clifford Algebras 7, 1 (1997)

    Article  MATH  MathSciNet  Google Scholar 

  35. Imaeda, K.: Prog. Theor. Phys. 5, 133 (1950)

    Article  MathSciNet  ADS  Google Scholar 

  36. Imaeda, K.: Nuovo Cimento B 32, 138 (1976)

    Article  MathSciNet  ADS  Google Scholar 

  37. Imaeda, K.: Nuovo Cimento B 50, 271 (1979)

    Article  MathSciNet  ADS  Google Scholar 

  38. Imaeda, K.: Nuovo Cimento Lett. 15, 91 (1976)

    Article  Google Scholar 

  39. Tachibana, H., Imaeda, K.: Nuovo Cimento B 104, 91 (1989)

    Article  MathSciNet  ADS  Google Scholar 

  40. Anderson, R., Joshi, G.C.: Phys. Essays 6, 308 (1993)

    Article  MathSciNet  Google Scholar 

  41. Singh, A.: Nuovo Cimento Lett. 31, 97 (1981)

    Article  Google Scholar 

  42. Singh, A.: Nuovo Cimento Lett. 31, 145 (1981)

    Article  Google Scholar 

  43. Majernik, V., Nagy, M.: Nuovo Cimento Lett. 16, 265 (1976)

    Article  MathSciNet  Google Scholar 

  44. Majernik, V., Nagy, M.: Adv. Appl. Clifford Algebras 9, 119 (1999)

    Article  MATH  MathSciNet  Google Scholar 

  45. Majernik, V.: Physica 39, 9 (2000)

    Google Scholar 

  46. Rajput, B.S., Kumar, S.R., Negi, O.P.S.: Nuovo Cimento Lett. 36, 75 (1983)

    Article  Google Scholar 

  47. Negi, O.P.S., Bisht, S., Bisht, P.S.: Il Nuovo Cimento B 113, 1449 (1998)

    MathSciNet  ADS  Google Scholar 

  48. Bisht, P.S., Negi, O.P.S., Rajput, B.S.: Ind. J. Pure Appl. Phys. 29, 457 (1991)

    Google Scholar 

  49. Bisht, P.S., Negi, O.P.S., Rajput, B.S.: Ind. J. Pure Appl. Phys. 28, 157 (1990)

    Google Scholar 

  50. Bisht, P.S., Negi, O.P.S., Rajput, B.S.: Indian J. Pure Appl. Phys. 24, 543 (1993)

    MathSciNet  Google Scholar 

  51. Kravchenko, V.V.: Applied Quaternionic Analysis. Research and Exposition in Mathematics, vol. 28. Heldermann, Berlin (2003)

    MATH  Google Scholar 

  52. Kravchenko, V.V.: Z. Anal. Anwend. 21, 21 (2002)

    MATH  MathSciNet  Google Scholar 

  53. Khmelnytskaya, V.K., Kravchenko, V.V.: Z. Anal. Anwend. 56, 4641 (2001)

    Google Scholar 

  54. Grudsky, S.M., Khmelnytskaya, K.V., Kravchenko, V.V.: J. Phys. A Math. Gen. 37, 4641 (2004)

    Article  MATH  MathSciNet  ADS  Google Scholar 

  55. Singh, J., Bisht, P.S., Negi, O.P.S.: Commun. Phys. 17, 83 (2007)

    Google Scholar 

  56. Singh, J., Bisht, P.S., Negi, O.P.S.: J. Phys. A: Math. Theor. 40, 9137 (2007)

    Article  MATH  MathSciNet  ADS  Google Scholar 

  57. Singh, J., Bisht, P.S., Negi, O.P.S.: Commun. Phys. 17, 129 (2007)

    Google Scholar 

  58. Singh, J., Bisht, P.S., Negi, O.P.S.: J. Phys. A: Math. Theor. 40, 11395 (2007)

    Article  MATH  MathSciNet  ADS  Google Scholar 

  59. Bisht, P.S., Singh, J., Negi, O.P.S.: In: Comsan, M.N.H. (ed.) Proceedings of 6th International Conference on Nuclear and Particle Physics, Egyptian Nuclear Physics Association, pp. 405–420, Luxor, Egypt from Nov. 17–21, 2007, (2008)

  60. Dangwal, S., Bisht, P.S., Negi, O.P.S.: Russ. Phys. J. 49, 1274 (2006)

    Article  MATH  Google Scholar 

  61. Bisht, P.S., Negi, O.P.S., Rajput, B.S.: Indian J. Pure Appl. Math. 31, 543 (1993)

    MathSciNet  Google Scholar 

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Correspondence to O. P. S. Negi.

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Bisht, P.S., Karnatak, G. & Negi, O.P.S. Generalized Gravi—Electromagnetism. Int J Theor Phys 49, 1344–1356 (2010). https://doi.org/10.1007/s10773-010-0315-4

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