Modular conjugation for the chiral fermion in multicomponent regions on the torus

Autores
Abate, Nicolás Bruno; Koifman, Mateo
Año de publicación
2023
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
We continue the study of the Tomita-Takesaki modular conjugation for a massless Dirac field in a generic multicomponent region in 1+1 spacetime dimensions. In this paper we focus on the computations for a thermal state on a circle, namely on the euclidean torus. By analytic continuation from the modular flow we arrive at an explicit expression for the modular conjugation in this scenario and derive its relevant limits. In contrast to the case of the vacuum on the line, this new result has a nonlocal behavior even for connected regions. It also presents a novel contribution coming from the purification one has to introduce in order to deal with a mixed state; a term that maps the algebra of operators of the region to a copy of the global one, the so-called “second world” algebra.
Fil: Abate, Nicolás Bruno. Comisión Nacional de Energía Atómica. Gerencia del Área de Energía Nuclear. Instituto Balseiro; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina
Fil: Koifman, Mateo. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Física de Buenos Aires. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Física de Buenos Aires; Argentina. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina
Materia
Entanglement
Quantum Field Theory
Dirac Field
Torus
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:11336/255091
Acceder
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oai_identifier_str oai:ri.conicet.gov.ar:11336/255091
network_acronym_str CONICETDig
repository_id_str 3498
network_name_str CONICET Digital (CONICET)
spelling Modular conjugation for the chiral fermion in multicomponent regions on the torusAbate, Nicolás BrunoKoifman, MateoEntanglementQuantum Field TheoryDirac FieldTorushttps://purl.org/becyt/ford/1.3https://purl.org/becyt/ford/1We continue the study of the Tomita-Takesaki modular conjugation for a massless Dirac field in a generic multicomponent region in 1+1 spacetime dimensions. In this paper we focus on the computations for a thermal state on a circle, namely on the euclidean torus. By analytic continuation from the modular flow we arrive at an explicit expression for the modular conjugation in this scenario and derive its relevant limits. In contrast to the case of the vacuum on the line, this new result has a nonlocal behavior even for connected regions. It also presents a novel contribution coming from the purification one has to introduce in order to deal with a mixed state; a term that maps the algebra of operators of the region to a copy of the global one, the so-called “second world” algebra.Fil: Abate, Nicolás Bruno. Comisión Nacional de Energía Atómica. Gerencia del Área de Energía Nuclear. Instituto Balseiro; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; ArgentinaFil: Koifman, Mateo. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Física de Buenos Aires. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Física de Buenos Aires; Argentina. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; ArgentinaAmerican Physical Society2023-10info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/pdfhttp://hdl.handle.net/11336/255091Abate, Nicolás Bruno; Koifman, Mateo; Modular conjugation for the chiral fermion in multicomponent regions on the torus; American Physical Society; Physical Review D; 108; 8; 10-2023; 1-122470-00102470-0029CONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/url/https://link.aps.org/doi/10.1103/PhysRevD.108.085003info:eu-repo/semantics/altIdentifier/doi/10.1103/PhysRevD.108.085003info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-sa/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-10-15T14:38:33Zoai:ri.conicet.gov.ar:11336/255091instacron: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 14:38:33.362CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv Modular conjugation for the chiral fermion in multicomponent regions on the torus
title Modular conjugation for the chiral fermion in multicomponent regions on the torus
spellingShingle Modular conjugation for the chiral fermion in multicomponent regions on the torus
Abate, Nicolás Bruno
Entanglement
Quantum Field Theory
Dirac Field
Torus
title_short Modular conjugation for the chiral fermion in multicomponent regions on the torus
title_full Modular conjugation for the chiral fermion in multicomponent regions on the torus
title_fullStr Modular conjugation for the chiral fermion in multicomponent regions on the torus
title_full_unstemmed Modular conjugation for the chiral fermion in multicomponent regions on the torus
title_sort Modular conjugation for the chiral fermion in multicomponent regions on the torus
dc.creator.none.fl_str_mv Abate, Nicolás Bruno
Koifman, Mateo
author Abate, Nicolás Bruno
author_facet Abate, Nicolás Bruno
Koifman, Mateo
author_role author
author2 Koifman, Mateo
author2_role author
dc.subject.none.fl_str_mv Entanglement
Quantum Field Theory
Dirac Field
Torus
topic Entanglement
Quantum Field Theory
Dirac Field
Torus
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 continue the study of the Tomita-Takesaki modular conjugation for a massless Dirac field in a generic multicomponent region in 1+1 spacetime dimensions. In this paper we focus on the computations for a thermal state on a circle, namely on the euclidean torus. By analytic continuation from the modular flow we arrive at an explicit expression for the modular conjugation in this scenario and derive its relevant limits. In contrast to the case of the vacuum on the line, this new result has a nonlocal behavior even for connected regions. It also presents a novel contribution coming from the purification one has to introduce in order to deal with a mixed state; a term that maps the algebra of operators of the region to a copy of the global one, the so-called “second world” algebra.
Fil: Abate, Nicolás Bruno. Comisión Nacional de Energía Atómica. Gerencia del Área de Energía Nuclear. Instituto Balseiro; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina
Fil: Koifman, Mateo. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Física de Buenos Aires. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Física de Buenos Aires; Argentina. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina
description We continue the study of the Tomita-Takesaki modular conjugation for a massless Dirac field in a generic multicomponent region in 1+1 spacetime dimensions. In this paper we focus on the computations for a thermal state on a circle, namely on the euclidean torus. By analytic continuation from the modular flow we arrive at an explicit expression for the modular conjugation in this scenario and derive its relevant limits. In contrast to the case of the vacuum on the line, this new result has a nonlocal behavior even for connected regions. It also presents a novel contribution coming from the purification one has to introduce in order to deal with a mixed state; a term that maps the algebra of operators of the region to a copy of the global one, the so-called “second world” algebra.
publishDate 2023
dc.date.none.fl_str_mv 2023-10
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/11336/255091
Abate, Nicolás Bruno; Koifman, Mateo; Modular conjugation for the chiral fermion in multicomponent regions on the torus; American Physical Society; Physical Review D; 108; 8; 10-2023; 1-12
2470-0010
2470-0029
CONICET Digital
CONICET
url http://hdl.handle.net/11336/255091
identifier_str_mv Abate, Nicolás Bruno; Koifman, Mateo; Modular conjugation for the chiral fermion in multicomponent regions on the torus; American Physical Society; Physical Review D; 108; 8; 10-2023; 1-12
2470-0010
2470-0029
CONICET Digital
CONICET
dc.language.none.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv info:eu-repo/semantics/altIdentifier/url/https://link.aps.org/doi/10.1103/PhysRevD.108.085003
info:eu-repo/semantics/altIdentifier/doi/10.1103/PhysRevD.108.085003
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
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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