A study of elliptic biquaternionic angular momentum and Dirac equation

Abstract

In this paper, we deal with the Dirac equation and angular momentum, which have an important place in physics in terms of elliptic biquaternions. Thanks to the elliptic biquaternionic representation of angular momentum, we have expressed some useful mathematical and physical results. We obtain the solutions of the Dirac equation with the help of Dirac matrices with elliptic biquaternionic structure. Then, we have expressed the elliptic biquaternionic rotational Dirac equation. This equation could be interpreted as the combination of rotational energy and angular momentum of the particle and anti-particle. Therefore, we also discuss the elliptic biquaternionic form of rotational energy–momentum and of the relativistic mass. Further, we express the spinor wave function by elliptic biquaternions. Accordingly, we also show elliptic biquaternionic rotational Dirac energy–momentum solutions through this function.