Biquaternion representation of the Dirack equations and bispinor fields

Abstract

Solutions of the biquaternion representation of the Dirac system of equations, the well-known equations of quantum mechanics, which are used to describe elementary particles, spinors and spinor fields, are constructed and investigated here. The Dirac equations belong to the classical equations of theoretical physics and are quite well studied. The biquaternionic form of the Dirac system of equations, which is its generalization and contains these equations as a special case, has been studied much less in the works of few authors and is mainly related to the group analysis of these equations or the construction of partial solutions. Works related to the construction of fundamental solutions of these equations and general solutions based on them, as in this work, are unknown to the author. Nonstationary and timeharmonic bispinors and bispinor fields in biquaternion representation are considered. These solutions of the Dirac bi-wave equation allow us to study the transformation of electric and gravimagnetic charges and currents under the influence of static external electro-gravimagnetic fields and describe the electrogravimagnetic fields generated by them, and can also find many useful applications in the study of EGM emitters of very different nature and shape. This can find many useful applications when studying EGM emitters of very different nature and shape.

Key words: algebra, biquaternion, biogradient, bi-wave equation, dirac equation.