Two Dimensional Representation of the Dirac Equation in Non-Associative Algebra

Affiliation(s)

Department of Physics and Mathematics, Faculty of Sciences, Lebanese University, Beirut, Lebanon.

Department of Physics and Mathematics, Faculty of Sciences, Lebanese University, Beirut, Lebanon.

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.

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.

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.

S. Hamieh and H. Abbas, "Two Dimensional Representation of the Dirac Equation in Non-Associative Algebra,"

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

[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