Approximate dual representation for Yang–Mills SU(2) gauge theory
Autor(a) principal: | |
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Data de Publicação: | 2018 |
Outros Autores: | , |
Tipo de documento: | Artigo |
Idioma: | eng |
Título da fonte: | Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) |
Texto Completo: | http://hdl.handle.net/10316/107591 https://doi.org/10.1140/epjc/s10052-018-6101-9 |
Resumo: | An approximate dual representation for non- Abelian lattice gauge theories in terms of a newset of dynamical variables, the plaquette occupation numbers (PONs) that are natural numbers, is discussed. They are the expansion indices of the local series of the expansion of the Boltzmann factors for every plaquette of the Yang–Mills action. After studying the constraints due to gauge symmetry, the SU(2) gauge theory is solved using Monte Carlo simulations. For a PONs configuration the weight factor is given by Haar-measure integrals over all links whose integrands are products of powers of plaquettes. Herein, updates are limited to changes of the PON at a plaquette or all PONs on a coordinate plane. The Markov chain transition probabilities are computed employing truncated maximal trees and the Metropolis algorithm. The algorithm performance is investigated with different types of updates for the plaquette mean value over a large range of βs.Using a 124 lattice very good agreement with a conventional heath bath algorithm is found for the strong and weak coupling limits. Deviations from the latter being below 0.1% for 2.5 < β < 3. The mass of the lightest J PC = 0++ glueball is evaluated and reproduces the results found in the literature. |
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Approximate dual representation for Yang–Mills SU(2) gauge theoryAn approximate dual representation for non- Abelian lattice gauge theories in terms of a newset of dynamical variables, the plaquette occupation numbers (PONs) that are natural numbers, is discussed. They are the expansion indices of the local series of the expansion of the Boltzmann factors for every plaquette of the Yang–Mills action. After studying the constraints due to gauge symmetry, the SU(2) gauge theory is solved using Monte Carlo simulations. For a PONs configuration the weight factor is given by Haar-measure integrals over all links whose integrands are products of powers of plaquettes. Herein, updates are limited to changes of the PON at a plaquette or all PONs on a coordinate plane. The Markov chain transition probabilities are computed employing truncated maximal trees and the Metropolis algorithm. The algorithm performance is investigated with different types of updates for the plaquette mean value over a large range of βs.Using a 124 lattice very good agreement with a conventional heath bath algorithm is found for the strong and weak coupling limits. Deviations from the latter being below 0.1% for 2.5 < β < 3. The mass of the lightest J PC = 0++ glueball is evaluated and reproduces the results found in the literature.The authors thank Paulo J. Silva for the heat bath data. This research was supported by computational resources supplied by the Center for Scientific Computing (NCC/GridUNESP) of the São Paulo State University (UNESP) and by the Departament of Physics of Coimbra University.Springer Nature2018info:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/articlehttp://hdl.handle.net/10316/107591http://hdl.handle.net/10316/107591https://doi.org/10.1140/epjc/s10052-018-6101-9eng1434-60441434-6052Leme, R.Oliveira, O.Krein, G.info:eu-repo/semantics/openAccessreponame:Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)instname:Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informaçãoinstacron:RCAAP2023-07-21T09:31:41Zoai:estudogeral.uc.pt:10316/107591Portal AgregadorONGhttps://www.rcaap.pt/oai/openaireopendoar:71602024-03-19T21:23:55.667053Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) - Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informaçãofalse |
dc.title.none.fl_str_mv |
Approximate dual representation for Yang–Mills SU(2) gauge theory |
title |
Approximate dual representation for Yang–Mills SU(2) gauge theory |
spellingShingle |
Approximate dual representation for Yang–Mills SU(2) gauge theory Leme, R. |
title_short |
Approximate dual representation for Yang–Mills SU(2) gauge theory |
title_full |
Approximate dual representation for Yang–Mills SU(2) gauge theory |
title_fullStr |
Approximate dual representation for Yang–Mills SU(2) gauge theory |
title_full_unstemmed |
Approximate dual representation for Yang–Mills SU(2) gauge theory |
title_sort |
Approximate dual representation for Yang–Mills SU(2) gauge theory |
author |
Leme, R. |
author_facet |
Leme, R. Oliveira, O. Krein, G. |
author_role |
author |
author2 |
Oliveira, O. Krein, G. |
author2_role |
author author |
dc.contributor.author.fl_str_mv |
Leme, R. Oliveira, O. Krein, G. |
description |
An approximate dual representation for non- Abelian lattice gauge theories in terms of a newset of dynamical variables, the plaquette occupation numbers (PONs) that are natural numbers, is discussed. They are the expansion indices of the local series of the expansion of the Boltzmann factors for every plaquette of the Yang–Mills action. After studying the constraints due to gauge symmetry, the SU(2) gauge theory is solved using Monte Carlo simulations. For a PONs configuration the weight factor is given by Haar-measure integrals over all links whose integrands are products of powers of plaquettes. Herein, updates are limited to changes of the PON at a plaquette or all PONs on a coordinate plane. The Markov chain transition probabilities are computed employing truncated maximal trees and the Metropolis algorithm. The algorithm performance is investigated with different types of updates for the plaquette mean value over a large range of βs.Using a 124 lattice very good agreement with a conventional heath bath algorithm is found for the strong and weak coupling limits. Deviations from the latter being below 0.1% for 2.5 < β < 3. The mass of the lightest J PC = 0++ glueball is evaluated and reproduces the results found in the literature. |
publishDate |
2018 |
dc.date.none.fl_str_mv |
2018 |
dc.type.status.fl_str_mv |
info:eu-repo/semantics/publishedVersion |
dc.type.driver.fl_str_mv |
info:eu-repo/semantics/article |
format |
article |
status_str |
publishedVersion |
dc.identifier.uri.fl_str_mv |
http://hdl.handle.net/10316/107591 http://hdl.handle.net/10316/107591 https://doi.org/10.1140/epjc/s10052-018-6101-9 |
url |
http://hdl.handle.net/10316/107591 https://doi.org/10.1140/epjc/s10052-018-6101-9 |
dc.language.iso.fl_str_mv |
eng |
language |
eng |
dc.relation.none.fl_str_mv |
1434-6044 1434-6052 |
dc.rights.driver.fl_str_mv |
info:eu-repo/semantics/openAccess |
eu_rights_str_mv |
openAccess |
dc.publisher.none.fl_str_mv |
Springer Nature |
publisher.none.fl_str_mv |
Springer Nature |
dc.source.none.fl_str_mv |
reponame:Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) instname:Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informação instacron:RCAAP |
instname_str |
Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informação |
instacron_str |
RCAAP |
institution |
RCAAP |
reponame_str |
Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) |
collection |
Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) |
repository.name.fl_str_mv |
Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) - Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informação |
repository.mail.fl_str_mv |
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_version_ |
1799134125201817600 |