Geometric Formulation of Electromagnetism
A new geometrical formulation of the theoretical foundations of classical electrodynamics is presented. This new geometrical approach is simultaneously based on Cartan's exterior calculus of differential forms and on the (Clifford) geometric algebra developed by David Hestenes (among others). However, instead of adopting the graded algebra of multivectors commonly used in geometric algebra, an alternative framework using a graded algebra of differential forms is introduced. Accordingly, such powerful tools as the exterior derivative and the (generalized) Stokes theorem can be used throughout. Within this framework a clear separation between even and odd (or pseudo) differential forms is then established from the beginning.
