Divergent Integrals Treatment in Quantum Field Theory
Main Author: | |
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Publication Date: | 2021 |
Other Authors: | |
Format: | Article |
Language: | eng |
Source: | Revista Brasileira de Ensino de Física (Online) |
Download full: | http://old.scielo.br/scielo.php?script=sci_arttext&pid=S1806-11172021000100407 |
Summary: | This paper presents a brief review on regularization methods and shows that the combination of two techniques could preserve symmetries in all orders of the Perturbation Theory. We will see, with two simple examples in the one-loop-order, what a regularization method needs to preserve symmetries. Furthermore, it will be shown that the problems with symmetry violations by regularization methods are related to the consequences of not being able to simply shift a variable in these divergent integrals. To facilitate the analysis between methods and provide analytical expressions for the finite parts of amplitudes, it was systematized in terms of a set of special functions. In the Appendix we introduce these functions and then cases of specific interest, functions continuity and some useful limits will be presented. |
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Divergent Integrals Treatment in Quantum Field TheoryPropagatorRegularizationThis paper presents a brief review on regularization methods and shows that the combination of two techniques could preserve symmetries in all orders of the Perturbation Theory. We will see, with two simple examples in the one-loop-order, what a regularization method needs to preserve symmetries. Furthermore, it will be shown that the problems with symmetry violations by regularization methods are related to the consequences of not being able to simply shift a variable in these divergent integrals. To facilitate the analysis between methods and provide analytical expressions for the finite parts of amplitudes, it was systematized in terms of a set of special functions. In the Appendix we introduce these functions and then cases of specific interest, functions continuity and some useful limits will be presented.Sociedade Brasileira de Física2021-01-01info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersiontext/htmlhttp://old.scielo.br/scielo.php?script=sci_arttext&pid=S1806-11172021000100407Revista Brasileira de Ensino de Física v.43 2021reponame:Revista Brasileira de Ensino de Física (Online)instname:Sociedade Brasileira de Física (SBF)instacron:SBF10.1590/1806-9126-rbef-2020-0380info:eu-repo/semantics/openAccessGobira,S. R.de Melo,M. D. B.eng2020-12-14T00:00:00Zoai:scielo:S1806-11172021000100407Revistahttp://www.sbfisica.org.br/rbef/https://old.scielo.br/oai/scielo-oai.php||marcio@sbfisica.org.br1806-91261806-1117opendoar:2020-12-14T00:00Revista Brasileira de Ensino de Física (Online) - Sociedade Brasileira de Física (SBF)false |
dc.title.none.fl_str_mv |
Divergent Integrals Treatment in Quantum Field Theory |
title |
Divergent Integrals Treatment in Quantum Field Theory |
spellingShingle |
Divergent Integrals Treatment in Quantum Field Theory Gobira,S. R. Propagator Regularization |
title_short |
Divergent Integrals Treatment in Quantum Field Theory |
title_full |
Divergent Integrals Treatment in Quantum Field Theory |
title_fullStr |
Divergent Integrals Treatment in Quantum Field Theory |
title_full_unstemmed |
Divergent Integrals Treatment in Quantum Field Theory |
title_sort |
Divergent Integrals Treatment in Quantum Field Theory |
author |
Gobira,S. R. |
author_facet |
Gobira,S. R. de Melo,M. D. B. |
author_role |
author |
author2 |
de Melo,M. D. B. |
author2_role |
author |
dc.contributor.author.fl_str_mv |
Gobira,S. R. de Melo,M. D. B. |
dc.subject.por.fl_str_mv |
Propagator Regularization |
topic |
Propagator Regularization |
description |
This paper presents a brief review on regularization methods and shows that the combination of two techniques could preserve symmetries in all orders of the Perturbation Theory. We will see, with two simple examples in the one-loop-order, what a regularization method needs to preserve symmetries. Furthermore, it will be shown that the problems with symmetry violations by regularization methods are related to the consequences of not being able to simply shift a variable in these divergent integrals. To facilitate the analysis between methods and provide analytical expressions for the finite parts of amplitudes, it was systematized in terms of a set of special functions. In the Appendix we introduce these functions and then cases of specific interest, functions continuity and some useful limits will be presented. |
publishDate |
2021 |
dc.date.none.fl_str_mv |
2021-01-01 |
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=S1806-11172021000100407 |
url |
http://old.scielo.br/scielo.php?script=sci_arttext&pid=S1806-11172021000100407 |
dc.language.iso.fl_str_mv |
eng |
language |
eng |
dc.relation.none.fl_str_mv |
10.1590/1806-9126-rbef-2020-0380 |
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.43 2021 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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1752122425184616448 |