Abstract
Quaternion Dirac equation has been analyzed and its supersymmetrization has been discussed consistently. It has been shown that the quaternion Dirac equation automatically describes the spin structure with its spin up and spin down components of two component quaternion Dirac spinors associated with positive and negative energies. It has also been shown that the supersymmetrization of quaternion Dirac equation works well for different cases associated with zero mass, nonzero mass, scalar potential and generalized electromagnetic potentials. Accordingly we have discussed the splitting of supersymmetrized Dirac equation in terms of electric and magnetic fields.
Similar content being viewed by others
References
Hamilton, W.R.: Elements of Quaternions. Chelsea, New York (1969)
Silberstein, L.: Philos. Mag. 63, 790 (1912)
Tait, P.G.: An Elementary Treatise on Quaternions. Oxford University Press, Oxford (1875)
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.: Physica 39, 9 (2000), and references therein
Adler, S.L.: Quaternion Quantum Mechanics and Quantum Fields. Oxford University Press, Oxford (1995)
Finklestein, D., Jauch, J.M., Schiminovich, S., Speiser, D.: J. Math. Phys. 4, 788 (1963)
Duc, D.V., Cuong, V.T.: Commun. Phys. 8, 197 (1998)
Morita, K.: Prog. Theor. Phys. 67, 1860 (1982)
Morita, K.: Prog. Theor. Phys. 65, 2071 (1981)
Bisht, P.S., Negi, O.P.S., Rajput, B.S.: Int. J. Theor. Phys. 32, 2099 (1993)
Davies, A.J.: Phys. Rev. A 49, 714 (1994)
Bisht, S., Bisht, P.S., Negi, O.P.S.: Nuovo Cimento B 113, 1449 (1998)
Waser, A.: AW-Verlag. www.aw-Verlag.ch (2000)
Kravchenkov, V.V.: Applied Quaternion Analysis. Helderman, Germany (2003)
Sohnius, M.F.: Phys. Rep. 128, 53 (1985)
Fayet, P., Ferrara, S.: Phys. Rep. 32, 247 (1977)
Cooper, F., Khare, A., Sukhatme, U.: Phys. Rep. 251, 267 (1995)
Kostelecky, V.A., Campbell, D.K.: Supersymmetry in Physics. North Holland, Amsterdam (1985)
Bilal, A.: Introduction to supersymmetry. hep-th/0101055
Witten, E.: Nucl. Phys. B 202, 213 (1982)
Hull, C.M.: The geometry of supersymmetric quantum mechanics. hep-th/9910028
Das, A., Okubo, S., Pernice, S.A.: Mod. Phys. Lett. A 12, 581 (1997)
Das, A., Okubo, S., Pernice, S.A.: Higher dimensional SUSY quantum mechanics. hep-th/9612125
Rajput, B.S., Joshi, D.C.: Hadron J. 4, 1805 (1981)
Rajput, B.S., Prakash, O.: Indian J. Phys. A 53, 274 (1979)
Roteli, P.: Mod. Phys. Lett. A 4, 933 (1989)
Roteli, P.: Mod. Phys. Lett. A 4, 1763 (1989)
Thaller, B.: The Dirac Equation. Springer, Berlin (1992)
Thaller, B.: The Dirac particle in magnetic field. In: Boutet de Monvel, A., Dita, P., Nenciu, G., Purice, R. (eds.) Recent Developments in Quantum Mechanics. Mathematical Physics Studies, vol. 12, pp. 351–366. Kluwer Academic, Dordrecht (1991)
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Rawat, S., Negi, O.P.S. Quaternion Dirac Equation and Supersymmetry. Int J Theor Phys 48, 2222–2234 (2009). https://doi.org/10.1007/s10773-009-0003-4
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10773-009-0003-4