Author(s)

Gregory Peter Wene

Department of Mathematics, The University of Texas at San Antonio, San Antonio, USA.

Hamieh and Abbas [1] propose using a 3-dimensional real algebra in a solution of the Dirac equation. We show that this algebra, denoted by , belongs to a large class of quadratic Jordan algebras with subalgebras isomorphic to the complex numbers and that the spinor matrices associated with the solution of the Dirac equation generate a six-dimensional real noncommutative Jordan algebra.

Dirac Equation; Jordan Algebra; Quadratic Algebra

G. Wene, "Algebras of Hamieh and Abbas Used in the Dirac Equation," Journal of Modern Physics, Vol. 3 No. 9, 2012, pp. 923-926. doi: 10.4236/jmp.2012.39120.