Generalized Split-Octonion Electrodynamics

Abstract

Starting with the usual definitions of octonions and split octonions in terms of Zorn vector matrix realization, we have made an attempt to write the consistent form of generalized Maxwell's equations in presence of electric and magnetic charges (dyons). We have thus written the generalized potential, generalized field, and generalized current of dyons in terms of split octonions and accordingly the split octonion forms of generalized Dirac Maxwell's equations are obtained in compact and consistent manner. This theory reproduces the dynamic of electric (magnetic) in the absence of magnetic (electric) charges.Comment: Abstract Key Words: Split octonions, Zorn Vector Matrix Realizations, Monopoles and dyons; Abstract PACS: 14.80 H

Split octonion reformulation of generalized linear gravitational field equations

“…So, we can express the split octonion algebra in terms of 2 × 2 Zorn's vector matrix components of which are scalar and vector parts of a quaternion, 23 i.e.,…”

“…For this case, we describe the unified field interaction of gravito-dyons and dyons in the modified GH and EM field. Furthermore, we have summarized the various split octonion equations for the case of the generalized GH-field of gravito-dyons in Table II. As such, Chanyal et al 22,23,26,39 have studied the generalized split octonion electromagnetic field of dyons and obtained the corresponding field equations and the equation of motion in a compact and simpler formulation. Thus, keeping in mind the dual nature of dyons, we also have summarized the various split octonion equations for the case of the generalized EM-field of dyons in the Table III.…”

Octonion Electrodynamics in Isotropic and Chiral Medium

“…In order to write the quantum equations of dyons in isotropic media in terms of compact notations of octonions, let us start with the four dimensional representation of differential operator [17,18] expressed in terms of octonion units as…”

“…In terms of the components of electric {A µ } and magnetic {B µ } four -potentials of dyons (particles carrying simultaneously the electric and magnetic charges), the octonionic potential is expressed in the isotropic medium as [17,18],…”

“…v is the generalized vector field of dyon in in isotropic medium [17,18]. Now applying the differential operator to the equation (30), we get…”