An Introduction to Space-Time Exterior Calculus
Mathematical Physics
2020-03-02 v1 math.MP
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.
Cite
@article{arxiv.2002.12604,
title = {An Introduction to Space-Time Exterior Calculus},
author = {Ivano Colombaro and Josep Font-Segura and Alfonso Martinez},
journal= {arXiv preprint arXiv:2002.12604},
year = {2020}
}
Comments
19 pages, 5 figures