Octonion symmetric Dirac--Maxwell equations

Abstract

We know that the octonion algebra is the largest division algebra. Therefore, we have discussed the octonion 8-dimensional space as the combination of 2 (external and internal) 4-dimensional spaces. The octonion wave equations in terms of 8 components has been written in terms of an 8 x 8 matrix. Octonion forms of potential as well as fields equations of dyons in terms of an 8 x 8 matrix are discussed in a consistent manner. At last, we have obtained the generalized Dirac-Maxwell equations of dyons in two 4-dimensional spaces, from the 8 x 8 matrix representation of octonion wave equations. Generalized Dirac-Maxwell equations are fully symmetric Maxwell's equations and allow for the possibility of magnetic charges and currents, i.e. analogous to electric charges and currents.