Exterior Calculus Perspective of Maxwell’s Electromagnetic Field Equations

Abstract

The classical Maxwell’s electromagnetic equations were obtained for electric field and magnetic field in terms of differential operators curl and divergence; these involve space coordinates and their directions, but use time as a parameter only. In Special Relativity time has been given the status of a coordinate and a direction is assigned. Using differential forms we have obtained in an entirely new way expressions for these differential operators which are invariant under Lorentz transformation: LT. Using these new derivations we obtain expressions for curl and divergence of electric field and magnetic field. These expressions are related to classical Maxwell’s equations in such a natural way that they lead again to the
conclusion that the latter are invariant under LT and provide an Exterior Calculus Perspective of Maxwell’s equations and their presentation from the point of view of 4-dimensional space time.