Maxwell’s Equations and Potentials in Dirac form using Geometric Algebra

Abstract

The basis for engineering electromagnetic computations still relies on Gibbs’ vector algebra. It is well known that Clifford algebra (geometric algebra) presents several enhancement on the latter. In this paper it is shown that Maxwell’s equations can be cast in a form similar to Dirac equation by using spinors. Additionally, a similar relation is derived for the fields and the potentials. It is also shown that, as a consequence of using the geometric algebra approach, the Lorenz gauge comes naturally from the grade structure.