On Léon van Hove's 1952 article on the foundations of Quantum Field Theory
Autor(a) principal: | |
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Data de Publicação: | 2020 |
Tipo de documento: | Artigo |
Idioma: | eng |
Título da fonte: | Revista Brasileira de Ensino de Física (Online) |
Texto Completo: | http://old.scielo.br/scielo.php?script=sci_arttext&pid=S1806-11172020000100400 |
Resumo: | In 1952, Léon van Hove published an article, in French, with the title Les difficultés de divergences pour um modèle particulier de champ quantifié. The article is frequently cited in relation to Haag's theorem and to the issue of the existence of unitarily inequivalent representations of the canonical commutation relations in Quantum Field Theory. Summarizing in brief, it suggests a link between the appearance of divergences in perturbative Quantum Field Theory and the fact that quantum states belonging to an interacting theory do not belong to the same Hilbert space of the free theory. It also suggests that renormalization fails to provide an accurate description of the time evolution of the quantum field, although it correctly accounts for the S matrix. Due to its relevance, and to the difficulty of finding an English translation, the ideas contained in this article are proposed again here, expanded with derivations and accompanied by a discussion aimed at putting the analysis into context. We highlight the main points from the perspective of a contemporary reader, and underline the differences with the standard approach usually taught in curricular courses in Quantum Field Theory. |
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On Léon van Hove's 1952 article on the foundations of Quantum Field TheoryQuantum Field TheoryPerturbative divergencesRenormalizationIn 1952, Léon van Hove published an article, in French, with the title Les difficultés de divergences pour um modèle particulier de champ quantifié. The article is frequently cited in relation to Haag's theorem and to the issue of the existence of unitarily inequivalent representations of the canonical commutation relations in Quantum Field Theory. Summarizing in brief, it suggests a link between the appearance of divergences in perturbative Quantum Field Theory and the fact that quantum states belonging to an interacting theory do not belong to the same Hilbert space of the free theory. It also suggests that renormalization fails to provide an accurate description of the time evolution of the quantum field, although it correctly accounts for the S matrix. Due to its relevance, and to the difficulty of finding an English translation, the ideas contained in this article are proposed again here, expanded with derivations and accompanied by a discussion aimed at putting the analysis into context. We highlight the main points from the perspective of a contemporary reader, and underline the differences with the standard approach usually taught in curricular courses in Quantum Field Theory.Sociedade Brasileira de Física2020-01-01info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersiontext/htmlhttp://old.scielo.br/scielo.php?script=sci_arttext&pid=S1806-11172020000100400Revista Brasileira de Ensino de Física v.42 2020reponame:Revista Brasileira de Ensino de Física (Online)instname:Sociedade Brasileira de Física (SBF)instacron:SBF10.1590/1806-9126-rbef-2020-0256info:eu-repo/semantics/openAccessSbisà,Fulvioeng2020-11-09T00:00:00Zoai:scielo:S1806-11172020000100400Revistahttp://www.sbfisica.org.br/rbef/https://old.scielo.br/oai/scielo-oai.php||marcio@sbfisica.org.br1806-91261806-1117opendoar:2020-11-09T00:00Revista Brasileira de Ensino de Física (Online) - Sociedade Brasileira de Física (SBF)false |
dc.title.none.fl_str_mv |
On Léon van Hove's 1952 article on the foundations of Quantum Field Theory |
title |
On Léon van Hove's 1952 article on the foundations of Quantum Field Theory |
spellingShingle |
On Léon van Hove's 1952 article on the foundations of Quantum Field Theory Sbisà,Fulvio Quantum Field Theory Perturbative divergences Renormalization |
title_short |
On Léon van Hove's 1952 article on the foundations of Quantum Field Theory |
title_full |
On Léon van Hove's 1952 article on the foundations of Quantum Field Theory |
title_fullStr |
On Léon van Hove's 1952 article on the foundations of Quantum Field Theory |
title_full_unstemmed |
On Léon van Hove's 1952 article on the foundations of Quantum Field Theory |
title_sort |
On Léon van Hove's 1952 article on the foundations of Quantum Field Theory |
author |
Sbisà,Fulvio |
author_facet |
Sbisà,Fulvio |
author_role |
author |
dc.contributor.author.fl_str_mv |
Sbisà,Fulvio |
dc.subject.por.fl_str_mv |
Quantum Field Theory Perturbative divergences Renormalization |
topic |
Quantum Field Theory Perturbative divergences Renormalization |
description |
In 1952, Léon van Hove published an article, in French, with the title Les difficultés de divergences pour um modèle particulier de champ quantifié. The article is frequently cited in relation to Haag's theorem and to the issue of the existence of unitarily inequivalent representations of the canonical commutation relations in Quantum Field Theory. Summarizing in brief, it suggests a link between the appearance of divergences in perturbative Quantum Field Theory and the fact that quantum states belonging to an interacting theory do not belong to the same Hilbert space of the free theory. It also suggests that renormalization fails to provide an accurate description of the time evolution of the quantum field, although it correctly accounts for the S matrix. Due to its relevance, and to the difficulty of finding an English translation, the ideas contained in this article are proposed again here, expanded with derivations and accompanied by a discussion aimed at putting the analysis into context. We highlight the main points from the perspective of a contemporary reader, and underline the differences with the standard approach usually taught in curricular courses in Quantum Field Theory. |
publishDate |
2020 |
dc.date.none.fl_str_mv |
2020-01-01 |
dc.type.driver.fl_str_mv |
info:eu-repo/semantics/article |
dc.type.status.fl_str_mv |
info:eu-repo/semantics/publishedVersion |
format |
article |
status_str |
publishedVersion |
dc.identifier.uri.fl_str_mv |
http://old.scielo.br/scielo.php?script=sci_arttext&pid=S1806-11172020000100400 |
url |
http://old.scielo.br/scielo.php?script=sci_arttext&pid=S1806-11172020000100400 |
dc.language.iso.fl_str_mv |
eng |
language |
eng |
dc.relation.none.fl_str_mv |
10.1590/1806-9126-rbef-2020-0256 |
dc.rights.driver.fl_str_mv |
info:eu-repo/semantics/openAccess |
eu_rights_str_mv |
openAccess |
dc.format.none.fl_str_mv |
text/html |
dc.publisher.none.fl_str_mv |
Sociedade Brasileira de Física |
publisher.none.fl_str_mv |
Sociedade Brasileira de Física |
dc.source.none.fl_str_mv |
Revista Brasileira de Ensino de Física v.42 2020 reponame:Revista Brasileira de Ensino de Física (Online) instname:Sociedade Brasileira de Física (SBF) instacron:SBF |
instname_str |
Sociedade Brasileira de Física (SBF) |
instacron_str |
SBF |
institution |
SBF |
reponame_str |
Revista Brasileira de Ensino de Física (Online) |
collection |
Revista Brasileira de Ensino de Física (Online) |
repository.name.fl_str_mv |
Revista Brasileira de Ensino de Física (Online) - Sociedade Brasileira de Física (SBF) |
repository.mail.fl_str_mv |
||marcio@sbfisica.org.br |
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1752122424431738880 |