An Introduction to Space–Time Exterior Calculus

Abstract

The basic concepts of exterior calculus for space−time multivectors are presented: Interior and exterior products, interior and exterior derivatives, oriented integrals over hypersurfaces, circulation and flux of multivector fields. Two Stokes theorems relating the exterior and interior derivatives with circulation and flux, respectively, are derived. As an application, it is shown how the exterior-calculus space−time formulation of the electromagnetic Maxwell equations and Lorentz force recovers the standard vector-calculus formulations, in both differential and integral forms.

Keywords

• exterior calculus
• exterior algebra
• electromagnetism
• Maxwell equations
• differential forms
• tensor calculus