Clifford Algebra and Electromagnetic Boundary Conditions At an Interface

Abstract

Electromagnetists use primarily vector algebra developed by Gibbs and Heaviside. However, there are other possibilities and of these probably the most attractive is Clifford algebra. Clifford algebra's elements can be interpreted as geometric entities and its operations as geometric transformations. As a consequence, electromagnetic boundary conditions at an interface can be cast in a geometric form. This form employs reflections with respect to a plane and gives a unified appearance to the boundary conditions in three-space and in space-time. Furthermore, in space-time the geometric form of the conditions is covariant.