An introduction to space–time exterior calculus
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- dc.contributor.author Colombaro, Ivano
- dc.contributor.author Font Segura, Josep
- dc.contributor.author Martinez, Alfonso
- dc.date.accessioned 2023-01-24T07:14:35Z
- dc.date.available 2023-01-24T07:14:35Z
- dc.date.issued 2019
- dc.description.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.
- dc.description.sponsorship This work has been funded in part by the Spanish Ministry of Economy and Competitiveness under grants TEC2016-78434-C3-1-R and BES-2017-081360.
- dc.format.mimetype application/pdf
- dc.identifier.citation Colombaro I, Font-Segura J, Martinez A. An introduction to space-time exterior calculus. Mathematics. 2019 Jun;7(6):564. DOI: 10.3390/math7060564
- dc.identifier.doi http://dx.doi.org/10.3390/math7060564
- dc.identifier.issn 2227-7390
- dc.identifier.uri http://hdl.handle.net/10230/55402
- dc.language.iso eng
- dc.publisher MDPI
- dc.relation.ispartof Mathematics. 2019 Jun;7(6):564
- dc.relation.projectID info:eu-repo/grantAgreement/ES/1PE/TEC2016-78434-C3-1-R
- dc.relation.projectID info:eu-repo/grantAgreement/ES/2PE/BES-2017-081360
- dc.rights © 2019 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).
- dc.rights.accessRights info:eu-repo/semantics/openAccess
- dc.rights.uri http://creativecommons.org/licenses/by/4.0/
- dc.subject.keyword Exterior calculus
- dc.subject.keyword Exterior algebra
- dc.subject.keyword Electromagnetism
- dc.subject.keyword Maxwell equations
- dc.subject.keyword Differential forms
- dc.subject.keyword Tensor calculus
- dc.title An introduction to space–time exterior calculus
- dc.type info:eu-repo/semantics/article
- dc.type.version info:eu-repo/semantics/publishedVersion