Two Dimensional Representation of the Dirac Equation in Non-Associative Algebra
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Abstract: In this note a simple extension of the complex algebra to higher dimension is proposed. Using the proposed algebra a two dimensional Dirac equation is formulated and its solution is calculated. It is found that there is a sub-algebra where the associative nature can be recovered.
Keywords:
Dirac Equation; Non-Associative Algebra
Cite this paper:
S. Hamieh and H. Abbas, "Two Dimensional Representation of the Dirac Equation in Non-Associative Algebra," Journal of Modern Physics, Vol. 3 No. 2, 2012, pp. 184-186. doi: 10.4236/jmp.2012.32025.
References
[1] S. L. Adler, “Quaternion Quantum Mechanics and Quantum Fields,” Oxford University Press, New York, 1995.
[2] G. Birkhoff and J. Neuman, “The Logic of Quantum Mechanics,” Annals of Mathematics, Vol. 37, No. 4, 1936, pp. 823-843. doi:10.2307/1968621
[3] D. Finkelstein, J. M. Jauch, S. Schiminovich and D. Spei- ser, “Foundations of Quaternion Quantum Mechanics,” Jour- nal of Mathematical Physics, Vol. 3, No. 2, 1962, pp. 207- 220. doi:10.1063/1.1703794
[4] A. A. Albert, “On a Certain Algebra of Quantum Mecha- nics,” Annals of Mathematics, Vol. 35, No. 1, 1934, pp. 65- 73. doi:10.2307/1968118