A new formulation of classical electrodynamics

Abstract

A new mathematical formulation of classical electrodynamics is presented. In the theory, the nature of Minkowski space, Lorentz transformations and Maxwell's equations is reduced to those of biquaternions and their functions, the theory of functions of a biquaternion variable. Maxwell's equations in vacuum become equivalent to the «regularity condition» for functions of a «real biquaternion» variable in the sense that Cauchy-Riemann equations are the regularity condition for functions of a complex variable. Several applications of the theory are given.