Non-perturbative λΦ4 in D=1+1: an example of the constructive quantum field theory approach in a schematic way

Autores
Gueron, Jorge; Leston, Mauricio
Año de publicación
2013
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
During the '70, several relativistic quantum field theory models in D = 1 + 1 and also in D = 2 + 1 have been constructed in a non-perturbative way. That was done in the so-called constructive quantum field theory approach, whose main results have been obtained by a clever use of Euclidean functional methods. Although in the construction of a single model there are several technical steps, some of them involving long proofs, the constructive quantum field theory approach contains conceptual insights about relativistic quantum field theory that deserved to be known and which are accessible without entering in technical details. The purpose of this note is to illustrate such insights by providing an oversimplified schematic exposition of the simple case of lambda(Phi)4 (with m > 0) in D = 1 + 1. Because of the absence of ultraviolet divergences in its perturbative version, this simple example , although does not capture all the difficulties in the constructive quantum field theory approach, allows to stress those difficulties inherent to the non-perturbative definition. We have made an effort in order to avoid several of the long technical intermediate steps without missing the main ideas and making contact with the usual language of the perturbative approach.
Fil: Gueron, Jorge. Universidad Católica Argentina. Facultad de Ciencias Fisico Matemáticas e Ingeniería. Departamento de Matemática; Argentina
Fil: Leston, Mauricio. Consejo Nacional de Investigaciónes Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Astronomía y Física del Espacio. - Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Astronomía y Física del Espacio; Argentina
Materia
FIELD THEORIES IN LOWER DIMENSIONS
NON PERTURBATIVES EFFECTS
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:11336/17036

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network_name_str CONICET Digital (CONICET)
spelling Non-perturbative λΦ4 in D=1+1: an example of the constructive quantum field theory approach in a schematic wayGueron, JorgeLeston, MauricioFIELD THEORIES IN LOWER DIMENSIONSNON PERTURBATIVES EFFECTShttps://purl.org/becyt/ford/1.3https://purl.org/becyt/ford/1During the '70, several relativistic quantum field theory models in D = 1 + 1 and also in D = 2 + 1 have been constructed in a non-perturbative way. That was done in the so-called constructive quantum field theory approach, whose main results have been obtained by a clever use of Euclidean functional methods. Although in the construction of a single model there are several technical steps, some of them involving long proofs, the constructive quantum field theory approach contains conceptual insights about relativistic quantum field theory that deserved to be known and which are accessible without entering in technical details. The purpose of this note is to illustrate such insights by providing an oversimplified schematic exposition of the simple case of lambda(Phi)4 (with m > 0) in D = 1 + 1. Because of the absence of ultraviolet divergences in its perturbative version, this simple example , although does not capture all the difficulties in the constructive quantum field theory approach, allows to stress those difficulties inherent to the non-perturbative definition. We have made an effort in order to avoid several of the long technical intermediate steps without missing the main ideas and making contact with the usual language of the perturbative approach.Fil: Gueron, Jorge. Universidad Católica Argentina. Facultad de Ciencias Fisico Matemáticas e Ingeniería. Departamento de Matemática; ArgentinaFil: Leston, Mauricio. Consejo Nacional de Investigaciónes Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Astronomía y Física del Espacio. - Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Astronomía y Física del Espacio; ArgentinaSpringer2013-08info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/pdfhttp://hdl.handle.net/11336/17036Gueron, Jorge; Leston, Mauricio; Non-perturbative λΦ4 in D=1+1: an example of the constructive quantum field theory approach in a schematic way; Springer; Journal Of High Energy Physics; 8; 52; 8-2013; 1-531029-8479enginfo:eu-repo/semantics/altIdentifier/url/https://link.springer.com/article/10.1007/JHEP08(2013)052info:eu-repo/semantics/altIdentifier/doi/10.1007/JHEP08(2013)052info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-sa/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-09-29T09:43:46Zoai:ri.conicet.gov.ar:11336/17036instacron: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:34982025-09-29 09:43:46.306CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv Non-perturbative λΦ4 in D=1+1: an example of the constructive quantum field theory approach in a schematic way
title Non-perturbative λΦ4 in D=1+1: an example of the constructive quantum field theory approach in a schematic way
spellingShingle Non-perturbative λΦ4 in D=1+1: an example of the constructive quantum field theory approach in a schematic way
Gueron, Jorge
FIELD THEORIES IN LOWER DIMENSIONS
NON PERTURBATIVES EFFECTS
title_short Non-perturbative λΦ4 in D=1+1: an example of the constructive quantum field theory approach in a schematic way
title_full Non-perturbative λΦ4 in D=1+1: an example of the constructive quantum field theory approach in a schematic way
title_fullStr Non-perturbative λΦ4 in D=1+1: an example of the constructive quantum field theory approach in a schematic way
title_full_unstemmed Non-perturbative λΦ4 in D=1+1: an example of the constructive quantum field theory approach in a schematic way
title_sort Non-perturbative λΦ4 in D=1+1: an example of the constructive quantum field theory approach in a schematic way
dc.creator.none.fl_str_mv Gueron, Jorge
Leston, Mauricio
author Gueron, Jorge
author_facet Gueron, Jorge
Leston, Mauricio
author_role author
author2 Leston, Mauricio
author2_role author
dc.subject.none.fl_str_mv FIELD THEORIES IN LOWER DIMENSIONS
NON PERTURBATIVES EFFECTS
topic FIELD THEORIES IN LOWER DIMENSIONS
NON PERTURBATIVES EFFECTS
purl_subject.fl_str_mv https://purl.org/becyt/ford/1.3
https://purl.org/becyt/ford/1
dc.description.none.fl_txt_mv During the '70, several relativistic quantum field theory models in D = 1 + 1 and also in D = 2 + 1 have been constructed in a non-perturbative way. That was done in the so-called constructive quantum field theory approach, whose main results have been obtained by a clever use of Euclidean functional methods. Although in the construction of a single model there are several technical steps, some of them involving long proofs, the constructive quantum field theory approach contains conceptual insights about relativistic quantum field theory that deserved to be known and which are accessible without entering in technical details. The purpose of this note is to illustrate such insights by providing an oversimplified schematic exposition of the simple case of lambda(Phi)4 (with m > 0) in D = 1 + 1. Because of the absence of ultraviolet divergences in its perturbative version, this simple example , although does not capture all the difficulties in the constructive quantum field theory approach, allows to stress those difficulties inherent to the non-perturbative definition. We have made an effort in order to avoid several of the long technical intermediate steps without missing the main ideas and making contact with the usual language of the perturbative approach.
Fil: Gueron, Jorge. Universidad Católica Argentina. Facultad de Ciencias Fisico Matemáticas e Ingeniería. Departamento de Matemática; Argentina
Fil: Leston, Mauricio. Consejo Nacional de Investigaciónes Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Astronomía y Física del Espacio. - Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Astronomía y Física del Espacio; Argentina
description During the '70, several relativistic quantum field theory models in D = 1 + 1 and also in D = 2 + 1 have been constructed in a non-perturbative way. That was done in the so-called constructive quantum field theory approach, whose main results have been obtained by a clever use of Euclidean functional methods. Although in the construction of a single model there are several technical steps, some of them involving long proofs, the constructive quantum field theory approach contains conceptual insights about relativistic quantum field theory that deserved to be known and which are accessible without entering in technical details. The purpose of this note is to illustrate such insights by providing an oversimplified schematic exposition of the simple case of lambda(Phi)4 (with m > 0) in D = 1 + 1. Because of the absence of ultraviolet divergences in its perturbative version, this simple example , although does not capture all the difficulties in the constructive quantum field theory approach, allows to stress those difficulties inherent to the non-perturbative definition. We have made an effort in order to avoid several of the long technical intermediate steps without missing the main ideas and making contact with the usual language of the perturbative approach.
publishDate 2013
dc.date.none.fl_str_mv 2013-08
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/11336/17036
Gueron, Jorge; Leston, Mauricio; Non-perturbative λΦ4 in D=1+1: an example of the constructive quantum field theory approach in a schematic way; Springer; Journal Of High Energy Physics; 8; 52; 8-2013; 1-53
1029-8479
url http://hdl.handle.net/11336/17036
identifier_str_mv Gueron, Jorge; Leston, Mauricio; Non-perturbative λΦ4 in D=1+1: an example of the constructive quantum field theory approach in a schematic way; Springer; Journal Of High Energy Physics; 8; 52; 8-2013; 1-53
1029-8479
dc.language.none.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv info:eu-repo/semantics/altIdentifier/url/https://link.springer.com/article/10.1007/JHEP08(2013)052
info:eu-repo/semantics/altIdentifier/doi/10.1007/JHEP08(2013)052
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 Springer
publisher.none.fl_str_mv Springer
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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