Abstract
We have made an attempt to reformulate the generalized field equation of dyons in terms of octonion variables. Octonion forms of generalized potential and current equations 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 electrodynamics in manifestly covariant and consistent manner.
Similar content being viewed by others
References
Dickson, L.E.: Ann. Math. 20, 155 (1919)
Hamilton, W.R.: Elements of Quaternions. Chelsea, New York (1969)
Tait, P.G.: An Elementary Treatise on Quaternions. Oxford University Press, Oxford (1875)
Finklestein, D., Jauch, J.M., Schiminovich, S., Speiser, D.: J. Math. Phys. 4, 788 (1963)
Adler, S.L.: Quaternion Quantum Mechanics and Quantum Fields. Oxford University Press, Oxford (1995)
Bisht, P.S., Negi, O.P.S., Rajput, B.S.: Prog. Theor. Phys. 85, 157 (1991)
Rajput, B.S., Kumar, S.R., Negi, O.P.S.: Lett. Nuovo Cimento 34, 180 (1982)
Rajput, B.S., Kumar, S.R., Negi, O.P.S.: Lett. Nuovo Cimento 36, 75 (1983)
Majernik, V.: Adv. Appl. Clifford Algebras 9, 119 (1999)
Majernik, V.: Physica 39, 9 (2000)
Kravchenkov, V.V.: Applied Quaternion Analysis. Helderman, Berlin (2003)
Bisht, S., Bisht, P.S., Negi, O.P.S.: Nuovo Cimento B 113, 1449 (1998)
Morita, K.: Prog. Theor. Phys. 67, 1860 (1982)
Morita, K.: Prog. Theor. Phys. 68, 2159 (1982)
Morita, K.: Prog. Theor. Phys. 65, 787 (1981)
Cayley, A.: Philos. Mag. 26, 208 (1845)
Graves, R.P.: Life of Sir William Rowan Hamilton. Arno Press, New York (1975), 3 volumes
Baez, J.C.: The octonions. Bull. Am. Math. Soc. 39, 145 (2001). arXiv:math.RA/0105155
Catto, S.: Exceptional projective geometries and internal symmetries. arXiv:hep-th/0302079
Catto, S.: In: Gruber, B. (ed.) Symmetries in Science, VI, p. 129. Plenum, New York (1993)
Catto, S., Gürsey, F.: Nuovo Cimento A 86, 201 (1985)
Catto, S., Gürsey, F.: Nuovo Cimento A 99, 685 (1988)
Günaydin, M., Gürsey, F.: Lett. Nuovo Cimento 6, 407 (1973)
Günaydin, M., Gürsey, F.: J. Math. Phys. 14, 1651 (1973)
Günaydin, M., Gürsey, F.: Phys. Rev. D 9, 3387 (1974)
Gürsey, F.: Non-associative algebras in quantum mechanics and particle physics. U. Virginia (1977)
Domokos, G., Kovesi-Domokos, S.: Phys. Rev. D 19, 2984 (1979)
Foot, R., Joshi, G.C.: Int. J. Theor. Phys. 28, 1449 (1989)
Foot, R., Joshi, G.C.: Phys. Lett. B 199, 203 (1987)
Kugo, T., Townsend, P.: Nucl. Phys. B 221, 357 (1983)
Manogue, C.A., Sudbery, A.: Phys. Rev. D 40, 4073 (1989)
Bernevig, B.A., Hu, J.P., Toumbus, N., Zhang, S.C.: Phys. Rev. Lett. 91, 23 (2003)
Evans, J.M.: Nucl. Phys. B 298, 92 (1988)
Lukierski, J., Toppan, F.: Phys. Lett. B 584, 315 (2004)
Lukierski, J., Toppan, F.: Phys. Lett. B 539, 266 (2002)
Schray, J.: Octonions and supersymmetry. Ph.D. thesis, Department of Physics, Oregon State University (1994)
Abdel-Khalek Mostafa, K.S.: Ring division algebras, self duality and supersymmetry. arXiv:hep-th/0002155
Imaeda, K., Tachibana, H., Imaeda, M.: Nuovo Cimento B 100, 53 (1987)
Imaeda, K., Tachibana, H., Imaeda, M.: Nuovo Cimento B 104, 91 (1989)
Imaeda, K., Tachibana, H., Imaeda, M.: Nuovo Cimento B 105, 1203 (1990)
Penny, R.: Am. J. Phys. 36, 871 (1968)
Penny, R.: Nuovo Cimento B 3, 95 (1971)
Gamba, A.: Nuovo Cimento A 111, 293 (1998)
Silagadze, Z.K.: Ann. Found. L. de Broglie 27, 241 (2002)
Gogberashvili, M.: J. Phys. A: Math. Gen. 39, 7099 (2006)
Tolan, T., Özdas, K., Tansili, M.: Nuovo Cimento B 121, 43 (2006)
Bisht, P.S., Negi, O.P.S.: Ind. J. Pure Appl. Phys. 31, 292 (1993)
Bisht, P.S., Negi, O.P.S.: Ind. J. Pure Appl. Phys. 32, 183 (1994)
Bisht, P.S., Negi, O.P.S.: Int. J. Theor. Phys. 47, 1497 (2008)
Bisht, P.S., Dangwal, S., Negi, O.P.S.: Int. J. Theor. Phys. 47, 2297 (2008)
Bisht, P.S., Pandey, B., Negi, O.P.S.: Octonion wave equation and generalized fields of dyons. In: T.M. Karade, G.S. Khadekar (eds.) Proc. National Symp. Mathematical Sciences, Nagpur, vol. 12, p. 137 (2001)
Bisht, P.S., Pandey, B., Negi, O.P.S.: Fizika B (Zagreb) 17, 405 (2008)
Bisht, P.S., Negi, O.P.S.: Pramana (India) 73, 105 (2009)
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Chanyal, B.C., Bisht, P.S. & Negi, O.P.S. Generalized Octonion Electrodynamics. Int J Theor Phys 49, 1333–1343 (2010). https://doi.org/10.1007/s10773-010-0314-5
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10773-010-0314-5