Biquaternionic representations of angular momentum and Dirac equation

Abstract

In the present article, after defining biquaternions, the general properties of biquaternion's algebra are introduced. The matrix representations of biquaternions are presented, as well. Then, the biquaternionic angular momentum is reformulated in terms of biquaternionic product. A new biquaternionic definition of the Dirac equation and its solution are given by the use of biquaternion's basis..