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Generalized Maxwell equations for exterior-algebra multivectors in (k, n) space-time dimensions

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dc.contributor.author Colombaro, Ivano
dc.contributor.author Font Segura, Josep
dc.contributor.author Martinez, Alfonso
dc.date.accessioned 2020-04-27T08:27:05Z
dc.date.available 2020-04-27T08:27:05Z
dc.date.issued 2020
dc.identifier.citation Colombaro I, Font Segura J, Martinez A. Generalized Maxwell equations for exterior-algebra multivectors in (k, n) space-time dimensions. Eur Phys J Plus. 2020 Mar 16;135:305. DOI: 10.1140/epjp/s13360-020-00305-y
dc.identifier.issn 2190-5444
dc.identifier.uri http://hdl.handle.net/10230/44332
dc.description.abstract This paper presents an exterior-algebra generalization of electromagnetic fields and source currents as multivectors of grades r and r−1, respectively, in a flat space-time with n space and k time dimensions. Formulas for the Maxwell equations and the Lorentz force for arbitrary values of r, n, and k are postulated in terms of interior and exterior derivatives, in a form that closely resembles their vector-calculus analogues. These formulas lead to solutions in terms of potentials of grade r−1, and to conservation laws in terms of a stress–energy–momentum tensor of rank 2 for any values of r, n, and k, for which a simple explicit formula is given. As an application, an expression for the flux of the stress–energy–momentum tensor across an (n+k−1)-dimensional slice of space-time is given in terms of the Fourier transform of the potentials. The abstraction of Maxwell equations with exterior calculus combines the simplicity and intuitiveness of vector calculus, as the formulas admit explicit expressions, with the power of tensors and differential forms, as the formulas can be given for any values of r, n, and k.
dc.description.sponsorship This work has been funded in part by the Spanish Ministry of Science, Innovation and Universities under Grants TEC2016-78434-C3-1-R and BES-2017-081360.
dc.format.mimetype application/pdf
dc.language.iso eng
dc.publisher Springer
dc.relation.ispartof The European Physical Journal Plus. 2020 Mar 16;135:305
dc.rights © Springer The final publication is available at Springer via http://dx.doi.org/10.1140/epjp/s13360-020-00305-y
dc.title Generalized Maxwell equations for exterior-algebra multivectors in (k, n) space-time dimensions
dc.type info:eu-repo/semantics/article
dc.identifier.doi http://dx.doi.org/10.1140/epjp/s13360-020-00305-y
dc.subject.keyword Multivectors
dc.subject.keyword Maxwell equations
dc.subject.keyword Stress-energy tensor
dc.subject.keyword Exterior algebra
dc.subject.keyword Exterior calculus
dc.subject.keyword Exterior calculus
dc.relation.projectID info:eu-repo/grantAgreement/ES/1PE/TEC2016-78434-C3-1-R
dc.rights.accessRights info:eu-repo/semantics/openAccess
dc.type.version info:eu-repo/semantics/acceptedVersion

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