Modular Hamiltonians on the null plane and the Markov property of the vacuum state

Autores
Casini, Horacio German; Testé Lino, Eduardo; Torroba, Gonzalo
Año de publicación
2017
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
We compute the modular Hamiltonians of regions having the future horizon lying on a null plane. For a CFT this is equivalent to regions with a boundary of arbitrary shape lying on the null cone. These Hamiltonians have a local expression on the horizon formed by integrals of the stress tensor. We prove this result in two different ways, and show that the modular Hamiltonians of these regions form an infinite dimensional Lie algebra. The corresponding group of unitary transformations moves the fields on the null surface locally along the null generators with arbitrary null line dependent velocities, but act non-locally outside the null plane. We regain this result in greater generality using more abstract tools on the algebraic quantum field theory. Finally, we show that modular Hamiltonians on the null surface satisfy a Markov property that leads to the saturation of the strong sub-additive inequality for the entropies and to the strong super-additivity of the relative entropy.
Fil: Casini, Horacio German. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Patagonia Norte; Argentina. Comisión Nacional de Energía Atómica. Centro Atómico Bariloche; Argentina
Fil: Testé Lino, Eduardo. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Patagonia Norte; Argentina. Comisión Nacional de Energía Atómica. Centro Atómico Bariloche; Argentina
Fil: Torroba, Gonzalo. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Patagonia Norte; Argentina. Comisión Nacional de Energía Atómica. Centro Atómico Bariloche; Argentina
Materia
ENTANGLEMENT ENTROPY
MARKOV PROPERTY
MODULAR HAMILTONIAN
NULL PLANE
Nivel de accesibilidad
acceso abierto
Condiciones de uso
https://creativecommons.org/licenses/by/2.5/ar/
Repositorio
CONICET Digital (CONICET)
Institución
Consejo Nacional de Investigaciones Científicas y Técnicas
OAI Identificador
oai:ri.conicet.gov.ar:11336/72688
Acceder
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oai_identifier_str oai:ri.conicet.gov.ar:11336/72688
network_acronym_str CONICETDig
repository_id_str 3498
network_name_str CONICET Digital (CONICET)
spelling Modular Hamiltonians on the null plane and the Markov property of the vacuum stateCasini, Horacio GermanTesté Lino, EduardoTorroba, GonzaloENTANGLEMENT ENTROPYMARKOV PROPERTYMODULAR HAMILTONIANNULL PLANEhttps://purl.org/becyt/ford/1.3https://purl.org/becyt/ford/1We compute the modular Hamiltonians of regions having the future horizon lying on a null plane. For a CFT this is equivalent to regions with a boundary of arbitrary shape lying on the null cone. These Hamiltonians have a local expression on the horizon formed by integrals of the stress tensor. We prove this result in two different ways, and show that the modular Hamiltonians of these regions form an infinite dimensional Lie algebra. The corresponding group of unitary transformations moves the fields on the null surface locally along the null generators with arbitrary null line dependent velocities, but act non-locally outside the null plane. We regain this result in greater generality using more abstract tools on the algebraic quantum field theory. Finally, we show that modular Hamiltonians on the null surface satisfy a Markov property that leads to the saturation of the strong sub-additive inequality for the entropies and to the strong super-additivity of the relative entropy.Fil: Casini, Horacio German. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Patagonia Norte; Argentina. Comisión Nacional de Energía Atómica. Centro Atómico Bariloche; ArgentinaFil: Testé Lino, Eduardo. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Patagonia Norte; Argentina. Comisión Nacional de Energía Atómica. Centro Atómico Bariloche; ArgentinaFil: Torroba, Gonzalo. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Patagonia Norte; Argentina. Comisión Nacional de Energía Atómica. Centro Atómico Bariloche; ArgentinaIOP Publishing2017-08-08info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/pdfapplication/pdfhttp://hdl.handle.net/11336/72688Casini, Horacio German; Testé Lino, Eduardo; Torroba, Gonzalo; Modular Hamiltonians on the null plane and the Markov property of the vacuum state; IOP Publishing; Journal of Physics A: Mathematical and Theoretical; 50; 36; 8-8-2017; 364001/1-291751-8113CONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/doi/10.1088/1751-8121/aa7eaainfo:eu-repo/semantics/altIdentifier/url/https://iopscience.iop.org/article/10.1088/1751-8121/aa7eaa/metainfo:eu-repo/semantics/altIdentifier/url/https://arxiv.org/abs/1703.10656info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-10-22T11:38:20Zoai:ri.conicet.gov.ar:11336/72688instacron: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:34982025-10-22 11:38:20.345CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv Modular Hamiltonians on the null plane and the Markov property of the vacuum state
title Modular Hamiltonians on the null plane and the Markov property of the vacuum state
spellingShingle Modular Hamiltonians on the null plane and the Markov property of the vacuum state
Casini, Horacio German
ENTANGLEMENT ENTROPY
MARKOV PROPERTY
MODULAR HAMILTONIAN
NULL PLANE
title_short Modular Hamiltonians on the null plane and the Markov property of the vacuum state
title_full Modular Hamiltonians on the null plane and the Markov property of the vacuum state
title_fullStr Modular Hamiltonians on the null plane and the Markov property of the vacuum state
title_full_unstemmed Modular Hamiltonians on the null plane and the Markov property of the vacuum state
title_sort Modular Hamiltonians on the null plane and the Markov property of the vacuum state
dc.creator.none.fl_str_mv Casini, Horacio German
Testé Lino, Eduardo
Torroba, Gonzalo
author Casini, Horacio German
author_facet Casini, Horacio German
Testé Lino, Eduardo
Torroba, Gonzalo
author_role author
author2 Testé Lino, Eduardo
Torroba, Gonzalo
author2_role author
author
dc.subject.none.fl_str_mv ENTANGLEMENT ENTROPY
MARKOV PROPERTY
MODULAR HAMILTONIAN
NULL PLANE
topic ENTANGLEMENT ENTROPY
MARKOV PROPERTY
MODULAR HAMILTONIAN
NULL PLANE
purl_subject.fl_str_mv https://purl.org/becyt/ford/1.3
https://purl.org/becyt/ford/1
dc.description.none.fl_txt_mv We compute the modular Hamiltonians of regions having the future horizon lying on a null plane. For a CFT this is equivalent to regions with a boundary of arbitrary shape lying on the null cone. These Hamiltonians have a local expression on the horizon formed by integrals of the stress tensor. We prove this result in two different ways, and show that the modular Hamiltonians of these regions form an infinite dimensional Lie algebra. The corresponding group of unitary transformations moves the fields on the null surface locally along the null generators with arbitrary null line dependent velocities, but act non-locally outside the null plane. We regain this result in greater generality using more abstract tools on the algebraic quantum field theory. Finally, we show that modular Hamiltonians on the null surface satisfy a Markov property that leads to the saturation of the strong sub-additive inequality for the entropies and to the strong super-additivity of the relative entropy.
Fil: Casini, Horacio German. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Patagonia Norte; Argentina. Comisión Nacional de Energía Atómica. Centro Atómico Bariloche; Argentina
Fil: Testé Lino, Eduardo. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Patagonia Norte; Argentina. Comisión Nacional de Energía Atómica. Centro Atómico Bariloche; Argentina
Fil: Torroba, Gonzalo. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Patagonia Norte; Argentina. Comisión Nacional de Energía Atómica. Centro Atómico Bariloche; Argentina
description We compute the modular Hamiltonians of regions having the future horizon lying on a null plane. For a CFT this is equivalent to regions with a boundary of arbitrary shape lying on the null cone. These Hamiltonians have a local expression on the horizon formed by integrals of the stress tensor. We prove this result in two different ways, and show that the modular Hamiltonians of these regions form an infinite dimensional Lie algebra. The corresponding group of unitary transformations moves the fields on the null surface locally along the null generators with arbitrary null line dependent velocities, but act non-locally outside the null plane. We regain this result in greater generality using more abstract tools on the algebraic quantum field theory. Finally, we show that modular Hamiltonians on the null surface satisfy a Markov property that leads to the saturation of the strong sub-additive inequality for the entropies and to the strong super-additivity of the relative entropy.
publishDate 2017
dc.date.none.fl_str_mv 2017-08-08
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/11336/72688
Casini, Horacio German; Testé Lino, Eduardo; Torroba, Gonzalo; Modular Hamiltonians on the null plane and the Markov property of the vacuum state; IOP Publishing; Journal of Physics A: Mathematical and Theoretical; 50; 36; 8-8-2017; 364001/1-29
1751-8113
CONICET Digital
CONICET
url http://hdl.handle.net/11336/72688
identifier_str_mv Casini, Horacio German; Testé Lino, Eduardo; Torroba, Gonzalo; Modular Hamiltonians on the null plane and the Markov property of the vacuum state; IOP Publishing; Journal of Physics A: Mathematical and Theoretical; 50; 36; 8-8-2017; 364001/1-29
1751-8113
CONICET Digital
CONICET
dc.language.none.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv info:eu-repo/semantics/altIdentifier/doi/10.1088/1751-8121/aa7eaa
info:eu-repo/semantics/altIdentifier/url/https://iopscience.iop.org/article/10.1088/1751-8121/aa7eaa/meta
info:eu-repo/semantics/altIdentifier/url/https://arxiv.org/abs/1703.10656
dc.rights.none.fl_str_mv info:eu-repo/semantics/openAccess
https://creativecommons.org/licenses/by/2.5/ar/
eu_rights_str_mv openAccess
rights_invalid_str_mv https://creativecommons.org/licenses/by/2.5/ar/
dc.format.none.fl_str_mv application/pdf
application/pdf
application/pdf
dc.publisher.none.fl_str_mv IOP Publishing
publisher.none.fl_str_mv IOP Publishing
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 12.982451

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