Nonlinear electrodynamics as a symmetric hyperbolic system

Autores
Abalos, Julio Fernando; Carrasco, Federico León; Goulart, Érico; Reula, Oscar Alejandro
Año de publicación
2015
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
Nonlinear theories generalizing Maxwell's electromagnetism and arising from a Lagrangian formalism have dispersion relations in which propagation planes factor into null planes corresponding to two effective metrics which depend on the pointwise values of the electromagnetic field. These effective Lorentzian metrics share the null (generically two) directions of the electromagnetic field. We show that the theory is symmetric hyperbolic if and only if the cones these metrics give rise to have a nonempty intersection, namely, that there exist families of symmetrizers in the sense of Geroch [26] which are positive definite for all covectors in the interior of the cones intersection. Thus, for these theories, the initial value problem is well posed. We illustrate the power of this approach with several nonlinear models of physical interest such as Born-Infeld, Gauss-Bonnet, and Euler-Heisenberg.
Fil: Abalos, Julio Fernando. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Córdoba. Instituto de Física Enrique Gaviola. Universidad Nacional de Córdoba. Instituto de Física Enrique Gaviola; Argentina. Universidad Nacional de Córdoba. Facultad de Matemática, Astronomía y Física; Argentina
Fil: Carrasco, Federico León. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Córdoba. Instituto de Física Enrique Gaviola. Universidad Nacional de Córdoba. Instituto de Física Enrique Gaviola; Argentina. Universidad Nacional de Córdoba. Facultad de Matemática, Astronomía y Física; Argentina
Fil: Goulart, Érico. CAPES Foundatio; Brasil
Fil: Reula, Oscar Alejandro. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Córdoba. Instituto de Física Enrique Gaviola. Universidad Nacional de Córdoba. Instituto de Física Enrique Gaviola; Argentina. Universidad Nacional de Córdoba. Facultad de Matemática, Astronomía y Física; Argentina
Materia
NONLINEAR ELECTRODYNAMICS
SYMMETRIC HYPERBOLIC
PARTIAL DIFFERENTIAL EQUATIONS
BORN INFELD
Nivel de accesibilidad
acceso abierto
Condiciones de uso
https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
Repositorio
CONICET Digital (CONICET)
Institución
Consejo Nacional de Investigaciones Científicas y Técnicas
OAI Identificador
oai:ri.conicet.gov.ar:11336/51184
Acceder
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oai_identifier_str oai:ri.conicet.gov.ar:11336/51184
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repository_id_str 3498
network_name_str CONICET Digital (CONICET)
spelling Nonlinear electrodynamics as a symmetric hyperbolic systemAbalos, Julio FernandoCarrasco, Federico LeónGoulart, ÉricoReula, Oscar AlejandroNONLINEAR ELECTRODYNAMICSSYMMETRIC HYPERBOLICPARTIAL DIFFERENTIAL EQUATIONSBORN INFELDhttps://purl.org/becyt/ford/1.3https://purl.org/becyt/ford/1Nonlinear theories generalizing Maxwell's electromagnetism and arising from a Lagrangian formalism have dispersion relations in which propagation planes factor into null planes corresponding to two effective metrics which depend on the pointwise values of the electromagnetic field. These effective Lorentzian metrics share the null (generically two) directions of the electromagnetic field. We show that the theory is symmetric hyperbolic if and only if the cones these metrics give rise to have a nonempty intersection, namely, that there exist families of symmetrizers in the sense of Geroch [26] which are positive definite for all covectors in the interior of the cones intersection. Thus, for these theories, the initial value problem is well posed. We illustrate the power of this approach with several nonlinear models of physical interest such as Born-Infeld, Gauss-Bonnet, and Euler-Heisenberg.Fil: Abalos, Julio Fernando. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Córdoba. Instituto de Física Enrique Gaviola. Universidad Nacional de Córdoba. Instituto de Física Enrique Gaviola; Argentina. Universidad Nacional de Córdoba. Facultad de Matemática, Astronomía y Física; ArgentinaFil: Carrasco, Federico León. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Córdoba. Instituto de Física Enrique Gaviola. Universidad Nacional de Córdoba. Instituto de Física Enrique Gaviola; Argentina. Universidad Nacional de Córdoba. Facultad de Matemática, Astronomía y Física; ArgentinaFil: Goulart, Érico. CAPES Foundatio; BrasilFil: Reula, Oscar Alejandro. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Córdoba. Instituto de Física Enrique Gaviola. Universidad Nacional de Córdoba. Instituto de Física Enrique Gaviola; Argentina. Universidad Nacional de Córdoba. Facultad de Matemática, Astronomía y Física; ArgentinaAmerican Physical Society2015-10info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/pdfapplication/pdfapplication/pdfhttp://hdl.handle.net/11336/51184Abalos, Julio Fernando; Carrasco, Federico León; Goulart, Érico; Reula, Oscar Alejandro; Nonlinear electrodynamics as a symmetric hyperbolic system; American Physical Society; Physical Review D: Particles, Fields, Gravitation and Cosmology; 92; 8; 10-2015; 1-191550-7998CONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/doi/10.1103/PhysRevD.92.084024info:eu-repo/semantics/altIdentifier/url/https://journals.aps.org/prd/abstract/10.1103/PhysRevD.92.084024info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-sa/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-10-15T14:31:56Zoai:ri.conicet.gov.ar:11336/51184instacron:CONICETInstitucionalhttp://ri.conicet.gov.ar/Organismo científico-tecnológicoNo correspondehttp://ri.conicet.gov.ar/oai/requestdasensio@conicet.gov.ar; lcarlino@conicet.gov.arArgentinaNo correspondeNo correspondeNo correspondeopendoar:34982025-10-15 14:31:56.829CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv Nonlinear electrodynamics as a symmetric hyperbolic system
title Nonlinear electrodynamics as a symmetric hyperbolic system
spellingShingle Nonlinear electrodynamics as a symmetric hyperbolic system
Abalos, Julio Fernando
NONLINEAR ELECTRODYNAMICS
SYMMETRIC HYPERBOLIC
PARTIAL DIFFERENTIAL EQUATIONS
BORN INFELD
title_short Nonlinear electrodynamics as a symmetric hyperbolic system
title_full Nonlinear electrodynamics as a symmetric hyperbolic system
title_fullStr Nonlinear electrodynamics as a symmetric hyperbolic system
title_full_unstemmed Nonlinear electrodynamics as a symmetric hyperbolic system
title_sort Nonlinear electrodynamics as a symmetric hyperbolic system
dc.creator.none.fl_str_mv Abalos, Julio Fernando
Carrasco, Federico León
Goulart, Érico
Reula, Oscar Alejandro
author Abalos, Julio Fernando
author_facet Abalos, Julio Fernando
Carrasco, Federico León
Goulart, Érico
Reula, Oscar Alejandro
author_role author
author2 Carrasco, Federico León
Goulart, Érico
Reula, Oscar Alejandro
author2_role author
author
author
dc.subject.none.fl_str_mv NONLINEAR ELECTRODYNAMICS
SYMMETRIC HYPERBOLIC
PARTIAL DIFFERENTIAL EQUATIONS
BORN INFELD
topic NONLINEAR ELECTRODYNAMICS
SYMMETRIC HYPERBOLIC
PARTIAL DIFFERENTIAL EQUATIONS
BORN INFELD
purl_subject.fl_str_mv https://purl.org/becyt/ford/1.3
https://purl.org/becyt/ford/1
dc.description.none.fl_txt_mv Nonlinear theories generalizing Maxwell's electromagnetism and arising from a Lagrangian formalism have dispersion relations in which propagation planes factor into null planes corresponding to two effective metrics which depend on the pointwise values of the electromagnetic field. These effective Lorentzian metrics share the null (generically two) directions of the electromagnetic field. We show that the theory is symmetric hyperbolic if and only if the cones these metrics give rise to have a nonempty intersection, namely, that there exist families of symmetrizers in the sense of Geroch [26] which are positive definite for all covectors in the interior of the cones intersection. Thus, for these theories, the initial value problem is well posed. We illustrate the power of this approach with several nonlinear models of physical interest such as Born-Infeld, Gauss-Bonnet, and Euler-Heisenberg.
Fil: Abalos, Julio Fernando. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Córdoba. Instituto de Física Enrique Gaviola. Universidad Nacional de Córdoba. Instituto de Física Enrique Gaviola; Argentina. Universidad Nacional de Córdoba. Facultad de Matemática, Astronomía y Física; Argentina
Fil: Carrasco, Federico León. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Córdoba. Instituto de Física Enrique Gaviola. Universidad Nacional de Córdoba. Instituto de Física Enrique Gaviola; Argentina. Universidad Nacional de Córdoba. Facultad de Matemática, Astronomía y Física; Argentina
Fil: Goulart, Érico. CAPES Foundatio; Brasil
Fil: Reula, Oscar Alejandro. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Córdoba. Instituto de Física Enrique Gaviola. Universidad Nacional de Córdoba. Instituto de Física Enrique Gaviola; Argentina. Universidad Nacional de Córdoba. Facultad de Matemática, Astronomía y Física; Argentina
description Nonlinear theories generalizing Maxwell's electromagnetism and arising from a Lagrangian formalism have dispersion relations in which propagation planes factor into null planes corresponding to two effective metrics which depend on the pointwise values of the electromagnetic field. These effective Lorentzian metrics share the null (generically two) directions of the electromagnetic field. We show that the theory is symmetric hyperbolic if and only if the cones these metrics give rise to have a nonempty intersection, namely, that there exist families of symmetrizers in the sense of Geroch [26] which are positive definite for all covectors in the interior of the cones intersection. Thus, for these theories, the initial value problem is well posed. We illustrate the power of this approach with several nonlinear models of physical interest such as Born-Infeld, Gauss-Bonnet, and Euler-Heisenberg.
publishDate 2015
dc.date.none.fl_str_mv 2015-10
dc.type.none.fl_str_mv info:eu-repo/semantics/article
info:eu-repo/semantics/publishedVersion
http://purl.org/coar/resource_type/c_6501
info:ar-repo/semantics/articulo
format article
status_str publishedVersion
dc.identifier.none.fl_str_mv http://hdl.handle.net/11336/51184
Abalos, Julio Fernando; Carrasco, Federico León; Goulart, Érico; Reula, Oscar Alejandro; Nonlinear electrodynamics as a symmetric hyperbolic system; American Physical Society; Physical Review D: Particles, Fields, Gravitation and Cosmology; 92; 8; 10-2015; 1-19
1550-7998
CONICET Digital
CONICET
url http://hdl.handle.net/11336/51184
identifier_str_mv Abalos, Julio Fernando; Carrasco, Federico León; Goulart, Érico; Reula, Oscar Alejandro; Nonlinear electrodynamics as a symmetric hyperbolic system; American Physical Society; Physical Review D: Particles, Fields, Gravitation and Cosmology; 92; 8; 10-2015; 1-19
1550-7998
CONICET Digital
CONICET
dc.language.none.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv info:eu-repo/semantics/altIdentifier/doi/10.1103/PhysRevD.92.084024
info:eu-repo/semantics/altIdentifier/url/https://journals.aps.org/prd/abstract/10.1103/PhysRevD.92.084024
dc.rights.none.fl_str_mv info:eu-repo/semantics/openAccess
https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
eu_rights_str_mv openAccess
rights_invalid_str_mv https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
dc.format.none.fl_str_mv application/pdf
application/pdf
application/pdf
application/pdf
dc.publisher.none.fl_str_mv American Physical Society
publisher.none.fl_str_mv American Physical Society
dc.source.none.fl_str_mv reponame:CONICET Digital (CONICET)
instname:Consejo Nacional de Investigaciones Científicas y Técnicas
reponame_str CONICET Digital (CONICET)
collection CONICET Digital (CONICET)
instname_str Consejo Nacional de Investigaciones Científicas y Técnicas
repository.name.fl_str_mv CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicas
repository.mail.fl_str_mv dasensio@conicet.gov.ar; lcarlino@conicet.gov.ar
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score 13.22299

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