Interpretations of Octonion Wave Equations

Abstract

The interpretations of octonion wave equations in eight dimensional space-time have been discussed. We have made an attempt to discuss the octonion field equation as the equation of motion for particles carrying simultaneously electric and magnetic charges (i.e. dyons) in external and internal spaces respectively. It has been concluded that the component of octonion potential wave equations behaves neither the generalized electromagnetic fields of monopoles nor the dyons. Rather, they have the mixed behaviour of electromagnetic fields associated with the electric and magnetic charges in external and internal spaces. We have also made an attempt to investigate the split octonion wave equation and its interpretation in classical electrodynamics and accordingly the consistent and compact forms of eight-dimensional potential and current equation of dyons are obtained in terms of Zorn's vector matrix realization of split octonions.Visualizing the external four space as the localization space for tachyons, it is shown that the split octonion wave equation reduces to the Maxwell's equation (field equation) for bradyons in R^{4}- space as well as that for tachyons in T^{4}- space in the absence of other.