An Introduction to Space–Time Exterior Calculus

Autor:	Ivano Colombaro, Josep Font-Segura, Alfonso Martinez
Jazyk:	angličtina
Rok vydání:	2019
Předmět:	exterior calculus exterior algebra electromagnetism Maxwell equations differential forms tensor calculus Mathematics QA1-939
Zdroj:	Mathematics, Vol 7, Iss 6, p 564 (2019)
Druh dokumentu:	article
ISSN:	2227-7390
DOI:	10.3390/math7060564
Popis:	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.
Databáze:	Directory of Open Access Journals
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