Derivation of the symmetric stress-energymomentum tensor in exterior algebra

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• dc.contributor.author Colombaro, Ivano
• dc.contributor.author Font Segura, Josep
• dc.contributor.author Martinez, Alfonso
• dc.date.accessioned 2023-02-01T13:27:56Z
• dc.date.available 2023-02-01T13:27:56Z
• dc.date.issued 2021
• dc.description.abstract We present a derivation of a manifestly symmetric form of the stress-energy-momentum using the mathematical tools of exterior algebra and exterior calculus, bypassing the standard symmetrizations of the canonical tensor. In a generalized flat space-time with arbitrary time and space dimensions, the tensor is found by evaluating the invariance of the action to infinitesimal space-time translations, using Lagrangian densities that are linear combinations of dot products of multivector fields. An interesting coordinate-free expression is provided for the divergence of the tensor, in terms of the interior and exterior derivatives of the multivector fields that form the Lagrangian density. A generalized Leibniz rule, applied to the variation of action, allows to obtain a conservation law for the derived stress-energy-momentum tensor. We finally show an application to the generalized theory of electromagnetism.
• 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.identifier.citation Colombaro I, Font-Segura J, Martinez A. Derivation of the symmetric stress-energymomentum tensor in exterior algebra. J Phys Conf Ser. 2021;2090:012050. DOI: 10.1088/1742-6596/2090/1/012050
• dc.identifier.doi http://dx.doi.org/10.1088/1742-6596/2090/1/012050
• dc.identifier.issn 1742-6588
• dc.identifier.uri http://hdl.handle.net/10230/55529
• dc.language.iso eng
• dc.publisher IOP Publishing Ltd.
• dc.relation.ispartof Journal of Physics: Conference Series. 2021;2090:012050.
• 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 Published under licence in Journal of Physics: Conference Series by IOP Publishing Ltd. Content from this work may be used under the terms of the Creative Commons Attribution 3.0 licence. Any further distribution of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI.
• dc.rights.accessRights info:eu-repo/semantics/openAccess
• dc.rights.uri http://creativecommons.org/licenses/by/3.0
• dc.subject.other Àlgebra
• dc.title Derivation of the symmetric stress-energymomentum tensor in exterior algebra
• dc.type info:eu-repo/semantics/article
• dc.type.version info:eu-repo/semantics/publishedVersion