An exterior-algebraic derivation of the symmetric stress–energy–momentum tensor in flat space–time

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• dc.contributor.author Martinez, Alfonso
• dc.contributor.author Font Segura, Josep
• dc.contributor.author Colombaro, Ivano
• dc.date.accessioned 2023-05-02T06:19:30Z
• dc.date.available 2023-05-02T06:19:30Z
• dc.date.issued 2021
• dc.description.abstract This paper characterizes the symmetric rank-2 stress–energy–momentum tensor associated with fields whose Lagrangian densities are expressed as the dot product of two multivector fields, e.g., scalar or gauge fields, in flat space–time. The tensor is derived by a direct application of exterior-algebraic methods to deal with the invariance of the action to infinitesimal space–time translations; this direct derivation avoids the use of the canonical tensor. Formulas for the tensor components and for the tensor itself are derived for generic values of the multivector grade s and of the number of time and space dimensions, k and n, respectively. A simple, coordinate-free, closed-form expression for the interior derivative (divergence) of the symmetric stress–energy–momentum tensor is also obtained: this expression provides a natural generalization of the Lorentz force that appears in the context of the electromagnetic theory. Applications of the formulas derived in this paper to the cases of generalized electromagnetism, Proca action, Yang–Mills fields and conformal invariance are briefly discussed.
• 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 Martinez A, Font-Segura J, Colombaro I. An exterior-algebraic derivation of the symmetric stress–energy–momentum tensor in flat space–time. Eur Phys J Plus. 2021;136(2):212. DOI: 10.1140/epjp/s13360-021-01192-7
• dc.identifier.doi http://dx.doi.org/10.1140/epjp/s13360-021-01192-7
• dc.identifier.issn 2190-5444
• dc.identifier.uri http://hdl.handle.net/10230/56632
• dc.language.iso eng
• dc.publisher Springer
• dc.relation.ispartof The European Physical Journal Plus. 2021;136(2):212.
• 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 © Springer The final publication is available at Springer via http://dx.doi.org/10.1140/epjp/s13360-021-01192-7
• dc.rights.accessRights info:eu-repo/semantics/openAccess
• dc.subject.other Àlgebra
• dc.subject.other Física
• dc.subject.other Electromagnetisme
• dc.title An exterior-algebraic derivation of the symmetric stress–energy–momentum tensor in flat space–time
• dc.type info:eu-repo/semantics/article
• dc.type.version info:eu-repo/semantics/acceptedVersion