Differential forms have long been used in the physics community in electromagnetics, quantum field theory, and other areas. Our work and that of others has shown that forms are also a powerful research tool for applied electromagnetics.
An area which we are exploring is the use of Green forms for anisotropic, inhomogeneous media. We modify the Hodge star operator to model the properties of a medium. This makes derivations simpler and more algebraic as compared to the usual vector/dyadic treatment, since entire tables of identities are replaced by a few general properties of the exterior derivative and the star operators. This work was presented at Antennas and Propagation Symposium (APS/URSI) 1996, Green Forms for Anisotropic, Inhomogeneous Media.
For other applications of differential forms, see our publications list.