A Complete Set of Conservation Laws of Dyons with the Clifford-Octonion Algebra

Abstract

The Clifford-octonion algebra is the highest hypercomplex algebra over a real field with Clifford coefficient (). The paper aims to apply the Clifford-octonion algebra (or simply called dualoctonion algebra) to describe the consistence theory of generalized electromagnetism and its conservation laws for dyons. The present paper describes the property of Lorentz invariance symmetries of dyons and their corresponding conservation laws. Moreover, we have studied the conservation of mass-energy, liner momentum, and angular momentum for four-dimensional particle dyons with the Clifford-octonion algebra. In generalized Clifford-octonion electromagnetic fields, we express the work-energy theorem and the linear momentum conservation theorem corresponding to the scalar and vector components of dyons, respectively. Finally, we have constructed the dual octonion form of the angular momentum conservation law, which represents an analog of the virial theorem in mechanics.