A Complete Set of Conservation Laws of Dyons with the Clifford-Octonion Algebra

  • B. C. Chanyal Department of Physics, G.B. Pant University of Agriculture & Technology
Keywords: dual octonion, dyons, angular momentum, conservation laws, virial theorem

Abstract

The Clifford-octonion algebra is the highest hypercomplex algebra over a real field with Clifford coefficient (

References

W.R. Hamilton. Elements of Quaternions (Chelsea, 1969).

P.G. Tait. An Elementary Treatise on Quaternions (Oxford Univ. Press, 1875).

R.P. Graves. Life of Sir William Rowan Hamilton (Arno Press, 1975).

J. Schray. Octonions and Supersymmetry. Ph. D. Thesis (Oregon State Univ., 1994).

A. Cayley. An Jacobi's elliptic functions, in reply to the Rev. B. Bornwin; and on quaternion. Phil. Mag. 26, 208 (1845).

J.C. Baez. The octonions. Bull. Amer. Math. Soc. 39, 145 (2001).

https://doi.org/10.1090/S0273-0979-01-00934-X

M. Tanı¸slı, M.E. Kansu. Octonionic Maxwell's equations for bi-isotropic media. J. Math. Phys. 52, 053511 (2011).

https://doi.org/10.1063/1.3582816

M. Tanı¸slı, M.E. Kansu, S. Demir. Reformulation of electromagnetic and gravito-electromagnetic equations for Lorentz system with octonion algebra. Gen. Relativ. Gravit. 46, (2014).

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

https://doi.org/10.1007/s10773-010-0314-5

B.C. Chanyal, P.S. Bisht, Li Tianjun, O.P S. Negi. Octonion quantum chromodynamics. Int. J. Theor. Phys. 51, 3410 (2012).

https://doi.org/10.1007/s10773-012-1222-7

J. Lukierski, F. Toppan, Generalized space-time supersymmetries, division algebras and octonionic M-theory. Phys. Lett. B 539, 266 (2002).

https://doi.org/10.1016/S0370-2693(02)02073-7

R. Foot, G.C. Joshi. Space-time symmetries of superstring and Jordan algebras. Int. J. Theor. Phys. 28, 1449 (1989).

https://doi.org/10.1007/BF00671588

W. Clifford. Preliminary sketch of biquaternions. Proc. London Math. Soc. 4, 381 (1873).

B.C. Chanyal, S.K. Chanyal, O. Bekta¸s, S. Y¨uce. A new approach on electromagnetism with dual number coefficient octonion algebra. Int. J. Geom. Meth. Mod. Phys. 13, 1630013 (2016).

https://doi.org/10.1142/S0219887816300130

B.C. Chanyal. Dual octonion electrodynamics with the massive field of dyons. J. Math. Phys. 57, 033503 (2016).

https://doi.org/10.1063/1.4943594

B.C. Chanyal, S.K. Chanyal. Dual number coefficient octonion algebra, field equations and conservation laws. Analysis Math. Phys. (2016), (Online Published).

R. Clausius. On a mechanical theorem applicable to heat. Phil. Magaz. 40, 122 (1870).

B.C. Chanyal. Octonion generalization of Pauli and Dirac matrices. Int. J. Geom. Meth. Mod. Phys. 12, 1550007 (2015).

https://doi.org/10.1142/S0219887815500073

B.C. Chanyal. Sedenion unified theory of gravi-electromagnetism. Indian J. Phys. 88, 1197 (2014).

https://doi.org/10.1007/s12648-014-0562-y

B.C. Chanyal, V.K. Sharma, O.P.S. Negi. Octonionic gravi-electromagnetism and dark matter. Int. J. Theor. Phys. 54, 3516 (2015).

https://doi.org/10.1007/s10773-015-2595-1

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

https://doi.org/10.1016/j.cjph.2017.01.003

Published
2018-12-15
How to Cite
Chanyal, B. (2018). A Complete Set of Conservation Laws of Dyons with the Clifford-Octonion Algebra. Ukrainian Journal of Physics, 62(6), 539. https://doi.org/10.15407/ujpe62.06.0539
Section
General problems of theoretical physics