Maxwell's equations in Clifford calculus framework -: An overview on the development

Quaternionic and Clifford calculus is applied on wide classes of problems in very different fields of science. The aim of our overview article is to line out the historical guidelines of electromagnetism in Clifford algebra framework. We want to introduce into the structure of low dimensional Clifford algebras and show the possibilities for the description of well-known terms in electromagnetics. Using Teodorescu transform we present an iteration procedure for solving Maxwell' s equations in isotropic homogeneous media. Assuming the so-called Drude-Born-Feodorov constitutive laws Maxwell' s equations in chiral media are formulated. Time-dependent problems are reduced to the consideration of Weyl operators and their right inverses the Teodorescu transforms. New tendencies are discussed.