An Introduction to Space–Time Exterior Calculus

Ivano Colombaro, Josep Font-Segura and Alfonso Martinez
Additional contact information
Ivano Colombaro: Department of Information and Communication Technologies, Universitat Pompeu Fabra, 08018 Barcelona, Spain
Josep Font-Segura: Department of Information and Communication Technologies, Universitat Pompeu Fabra, 08018 Barcelona, Spain
Alfonso Martinez: Department of Information and Communication Technologies, Universitat Pompeu Fabra, 08018 Barcelona, Spain

Mathematics, 2019, vol. 7, issue 6, 1-20

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 (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2019
References: View complete reference list from CitEc
Citations:

Downloads: (external link)
https://www.mdpi.com/2227-7390/7/6/564/pdf (application/pdf)
https://www.mdpi.com/2227-7390/7/6/564/ (text/html)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:gam:jmathe:v:7:y:2019:i:6:p:564-:d:242093

Access Statistics for this article

Mathematics is currently edited by Ms. Emma He

More articles in Mathematics from MDPI
Bibliographic data for series maintained by MDPI Indexing Manager ().