Polyharmonic green functions and nonlocal Bondi-Metzner-Sachs transformations of a free scalar field

We express the nonlocal Bondi-Metzner-Sachs (BMS) charges of a free massless Klein-Gordon scalar field in 2 þ 1 in terms of the Green functions of the polyharmonic operators. Using the properties of these Green functions, we are able to discuss the asymptotic behavior of the fields that ensures the...

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Detalles Bibliográficos
Autores: Batlle Arnau, Carles|||0000-0002-6088-6187, Campello, Víctor, Gomis Torné, Joaquim
Tipo de recurso: artículo
Fecha de publicación:2023
País:España
Institución:Universitat Politècnica de Catalunya (UPC)
Repositorio:UPCommons. Portal del coneixement obert de la UPC
Idioma:inglés
OAI Identifier:oai:upcommons.upc.edu:2117/380745
Acceso en línea:https://hdl.handle.net/2117/380745
https://dx.doi.org/10.1103/PhysRevD.107.025010
Access Level:acceso abierto
Palabra clave:Symmetry (Mathematics)
Harmonic functions
BMS symmetry
Nonlocal transformations
Polyharmonic functions
Simetria (Matemàtica)
Funcions harmòniques
Àrees temàtiques de la UPC::Matemàtiques i estadística::Àlgebra
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spelling Polyharmonic green functions and nonlocal Bondi-Metzner-Sachs transformations of a free scalar fieldBatlle Arnau, Carles|||0000-0002-6088-6187Campello, VíctorGomis Torné, JoaquimSymmetry (Mathematics)Harmonic functionsBMS symmetryNonlocal transformationsPolyharmonic functionsSimetria (Matemàtica)Funcions harmòniquesÀrees temàtiques de la UPC::Matemàtiques i estadística::ÀlgebraWe express the nonlocal Bondi-Metzner-Sachs (BMS) charges of a free massless Klein-Gordon scalar field in 2 þ 1 in terms of the Green functions of the polyharmonic operators. Using the properties of these Green functions, we are able to discuss the asymptotic behavior of the fields that ensures the existence of the charges and prove that one obtains a realization of the 2 þ 1 BMS algebra in canonical phase space. We also discuss the transformations in configuration space and show that in this case the algebra closes only up to skew-symmetric combinations of the equations of motion. The formulation of the charges in terms of Green functions opens the way to the generalization of the formalism to other dimensions and systems.We acknowledge discussions with Marc Henneaux and Axel Kleinschmidt. The work of C. B. is partially supported by the Project MASHED (Grant No. TED2021-129927BI00), funded by Grant No. MCIN/AEI/10.13039/ 501100011033 and by the European Union Next Generation EU/PRTR. J. G. has been supported in part by Grants No. MINECO FPA2016-76005-C2-1-P and No. PID2019-105614 GB-C21 and from the State Agency for Research of the Spanish Ministry of Science and Innovation through the Unit of Excellence Maria de Maeztu 2020–2023 award to the Institute of Cosmos Sciences (Grant No. CEX2019-000918-M).Peer ReviewedAmerican Physical Society (APS)20232023-01-1720232023-01-19journal articlehttp://purl.org/coar/resource_type/c_6501VoRhttp://purl.org/coar/version/c_970fb48d4fbd8a85info:eu-repo/semantics/articleapplication/pdfapplication/pdfhttps://hdl.handle.net/2117/380745https://dx.doi.org/10.1103/PhysRevD.107.025010reponame:UPCommons. Portal del coneixement obert de la UPCinstname:Universitat Politècnica de Catalunya (UPC)Inglésengopen accesshttp://purl.org/coar/access_right/c_abf2Attribution 4.0 Internationalhttp://creativecommons.org/licenses/by/4.0/info:eu-repo/semantics/openAccessoai:upcommons.upc.edu:2117/3807452026-05-27T15:37:01Z
dc.title.none.fl_str_mv Polyharmonic green functions and nonlocal Bondi-Metzner-Sachs transformations of a free scalar field
title Polyharmonic green functions and nonlocal Bondi-Metzner-Sachs transformations of a free scalar field
spellingShingle Polyharmonic green functions and nonlocal Bondi-Metzner-Sachs transformations of a free scalar field
Batlle Arnau, Carles|||0000-0002-6088-6187
Symmetry (Mathematics)
Harmonic functions
BMS symmetry
Nonlocal transformations
Polyharmonic functions
Simetria (Matemàtica)
Funcions harmòniques
Àrees temàtiques de la UPC::Matemàtiques i estadística::Àlgebra
title_short Polyharmonic green functions and nonlocal Bondi-Metzner-Sachs transformations of a free scalar field
title_full Polyharmonic green functions and nonlocal Bondi-Metzner-Sachs transformations of a free scalar field
title_fullStr Polyharmonic green functions and nonlocal Bondi-Metzner-Sachs transformations of a free scalar field
title_full_unstemmed Polyharmonic green functions and nonlocal Bondi-Metzner-Sachs transformations of a free scalar field
title_sort Polyharmonic green functions and nonlocal Bondi-Metzner-Sachs transformations of a free scalar field
dc.creator.none.fl_str_mv Batlle Arnau, Carles|||0000-0002-6088-6187
Campello, Víctor
Gomis Torné, Joaquim
author Batlle Arnau, Carles|||0000-0002-6088-6187
author_facet Batlle Arnau, Carles|||0000-0002-6088-6187
Campello, Víctor
Gomis Torné, Joaquim
author_role author
author2 Campello, Víctor
Gomis Torné, Joaquim
author2_role author
author
dc.subject.none.fl_str_mv Symmetry (Mathematics)
Harmonic functions
BMS symmetry
Nonlocal transformations
Polyharmonic functions
Simetria (Matemàtica)
Funcions harmòniques
Àrees temàtiques de la UPC::Matemàtiques i estadística::Àlgebra
topic Symmetry (Mathematics)
Harmonic functions
BMS symmetry
Nonlocal transformations
Polyharmonic functions
Simetria (Matemàtica)
Funcions harmòniques
Àrees temàtiques de la UPC::Matemàtiques i estadística::Àlgebra
description We express the nonlocal Bondi-Metzner-Sachs (BMS) charges of a free massless Klein-Gordon scalar field in 2 þ 1 in terms of the Green functions of the polyharmonic operators. Using the properties of these Green functions, we are able to discuss the asymptotic behavior of the fields that ensures the existence of the charges and prove that one obtains a realization of the 2 þ 1 BMS algebra in canonical phase space. We also discuss the transformations in configuration space and show that in this case the algebra closes only up to skew-symmetric combinations of the equations of motion. The formulation of the charges in terms of Green functions opens the way to the generalization of the formalism to other dimensions and systems.
publishDate 2023
dc.date.none.fl_str_mv 2023
2023-01-17
2023
2023-01-19
dc.type.none.fl_str_mv journal article
http://purl.org/coar/resource_type/c_6501
VoR
http://purl.org/coar/version/c_970fb48d4fbd8a85
dc.type.openaire.fl_str_mv info:eu-repo/semantics/article
format article
dc.identifier.none.fl_str_mv https://hdl.handle.net/2117/380745
https://dx.doi.org/10.1103/PhysRevD.107.025010
url https://hdl.handle.net/2117/380745
https://dx.doi.org/10.1103/PhysRevD.107.025010
dc.language.none.fl_str_mv Inglés
eng
language_invalid_str_mv Inglés
language eng
dc.rights.none.fl_str_mv open access
http://purl.org/coar/access_right/c_abf2
Attribution 4.0 International
http://creativecommons.org/licenses/by/4.0/
dc.rights.openaire.fl_str_mv info:eu-repo/semantics/openAccess
rights_invalid_str_mv open access
http://purl.org/coar/access_right/c_abf2
Attribution 4.0 International
http://creativecommons.org/licenses/by/4.0/
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv application/pdf
application/pdf
dc.publisher.none.fl_str_mv American Physical Society (APS)
publisher.none.fl_str_mv American Physical Society (APS)
dc.source.none.fl_str_mv reponame:UPCommons. Portal del coneixement obert de la UPC
instname:Universitat Politècnica de Catalunya (UPC)
instname_str Universitat Politècnica de Catalunya (UPC)
reponame_str UPCommons. Portal del coneixement obert de la UPC
collection UPCommons. Portal del coneixement obert de la UPC
repository.name.fl_str_mv
repository.mail.fl_str_mv
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score 15.300719

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