Fluctuating Dimension in a Discrete Model for Quantum Gravity Based on the Spectral Principle
Autor(a) principal: | |
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Data de Publicação: | 2003 |
Outros Autores: | , |
Tipo de documento: | Artigo |
Idioma: | eng |
Título da fonte: | Repositório Institucional da UNESP |
Texto Completo: | http://dx.doi.org/10.1103/PhysRevLett.91.081301 http://hdl.handle.net/11449/219295 |
Resumo: | The spectral principle of Connes and Chamseddine is used as a starting point to define a discrete model for Euclidean quantum gravity. Instead of summing over ordinary geometries, we consider the sum over generalized geometries where topology, metric, and dimension can fluctuate. The model describes the geometry of spaces with a countable number [Formula presented] of points, and is related to the Gaussian unitary ensemble of Hermitian matrices. We show that this simple model has two phases. The expectation value [Formula presented], the average number of points in the Universe, is finite in one phase and diverges in the other. We compute the critical point as well as the critical exponent of [Formula presented]. Moreover, the space-time dimension [Formula presented] is a dynamical observable in our model, and plays the role of an order parameter. The computation of [Formula presented] is discussed and an upper bound is found, [Formula presented]. © 2003 The American Physical Society. |
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Repositório Institucional da UNESP |
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Fluctuating Dimension in a Discrete Model for Quantum Gravity Based on the Spectral PrincipleThe spectral principle of Connes and Chamseddine is used as a starting point to define a discrete model for Euclidean quantum gravity. Instead of summing over ordinary geometries, we consider the sum over generalized geometries where topology, metric, and dimension can fluctuate. The model describes the geometry of spaces with a countable number [Formula presented] of points, and is related to the Gaussian unitary ensemble of Hermitian matrices. We show that this simple model has two phases. The expectation value [Formula presented], the average number of points in the Universe, is finite in one phase and diverges in the other. We compute the critical point as well as the critical exponent of [Formula presented]. Moreover, the space-time dimension [Formula presented] is a dynamical observable in our model, and plays the role of an order parameter. The computation of [Formula presented] is discussed and an upper bound is found, [Formula presented]. © 2003 The American Physical Society.Faculdade de Tecnologia de São Paulo-DEG-CEETEPS-UNESP Praça Fernando Prestes, São Paulo, 01124-060Universidade de São Paulo Instituto de Física-DFMA, Caixa Postal 66318, 05315-970Faculdade de Tecnologia de São Paulo-DEG-CEETEPS-UNESP Praça Fernando Prestes, São Paulo, 01124-060Universidade Estadual Paulista (UNESP)Universidade de São Paulo (USP)de Albuquerque, Luiz C. [UNESP]deLyra, Jorge L.Teotonio-Sobrinho, Paulo2022-04-28T18:54:43Z2022-04-28T18:54:43Z2003-08-22info:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/articlehttp://dx.doi.org/10.1103/PhysRevLett.91.081301Physical Review Letters, v. 91, n. 8, 2003.1079-71140031-9007http://hdl.handle.net/11449/21929510.1103/PhysRevLett.91.0813012-s2.0-0141973590Scopusreponame:Repositório Institucional da UNESPinstname:Universidade Estadual Paulista (UNESP)instacron:UNESPengPhysical Review Lettersinfo:eu-repo/semantics/openAccess2022-04-28T18:54:43Zoai:repositorio.unesp.br:11449/219295Repositório InstitucionalPUBhttp://repositorio.unesp.br/oai/requestopendoar:29462024-08-05T23:41:20.851266Repositório Institucional da UNESP - Universidade Estadual Paulista (UNESP)false |
dc.title.none.fl_str_mv |
Fluctuating Dimension in a Discrete Model for Quantum Gravity Based on the Spectral Principle |
title |
Fluctuating Dimension in a Discrete Model for Quantum Gravity Based on the Spectral Principle |
spellingShingle |
Fluctuating Dimension in a Discrete Model for Quantum Gravity Based on the Spectral Principle de Albuquerque, Luiz C. [UNESP] |
title_short |
Fluctuating Dimension in a Discrete Model for Quantum Gravity Based on the Spectral Principle |
title_full |
Fluctuating Dimension in a Discrete Model for Quantum Gravity Based on the Spectral Principle |
title_fullStr |
Fluctuating Dimension in a Discrete Model for Quantum Gravity Based on the Spectral Principle |
title_full_unstemmed |
Fluctuating Dimension in a Discrete Model for Quantum Gravity Based on the Spectral Principle |
title_sort |
Fluctuating Dimension in a Discrete Model for Quantum Gravity Based on the Spectral Principle |
author |
de Albuquerque, Luiz C. [UNESP] |
author_facet |
de Albuquerque, Luiz C. [UNESP] deLyra, Jorge L. Teotonio-Sobrinho, Paulo |
author_role |
author |
author2 |
deLyra, Jorge L. Teotonio-Sobrinho, Paulo |
author2_role |
author author |
dc.contributor.none.fl_str_mv |
Universidade Estadual Paulista (UNESP) Universidade de São Paulo (USP) |
dc.contributor.author.fl_str_mv |
de Albuquerque, Luiz C. [UNESP] deLyra, Jorge L. Teotonio-Sobrinho, Paulo |
description |
The spectral principle of Connes and Chamseddine is used as a starting point to define a discrete model for Euclidean quantum gravity. Instead of summing over ordinary geometries, we consider the sum over generalized geometries where topology, metric, and dimension can fluctuate. The model describes the geometry of spaces with a countable number [Formula presented] of points, and is related to the Gaussian unitary ensemble of Hermitian matrices. We show that this simple model has two phases. The expectation value [Formula presented], the average number of points in the Universe, is finite in one phase and diverges in the other. We compute the critical point as well as the critical exponent of [Formula presented]. Moreover, the space-time dimension [Formula presented] is a dynamical observable in our model, and plays the role of an order parameter. The computation of [Formula presented] is discussed and an upper bound is found, [Formula presented]. © 2003 The American Physical Society. |
publishDate |
2003 |
dc.date.none.fl_str_mv |
2003-08-22 2022-04-28T18:54:43Z 2022-04-28T18:54:43Z |
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://dx.doi.org/10.1103/PhysRevLett.91.081301 Physical Review Letters, v. 91, n. 8, 2003. 1079-7114 0031-9007 http://hdl.handle.net/11449/219295 10.1103/PhysRevLett.91.081301 2-s2.0-0141973590 |
url |
http://dx.doi.org/10.1103/PhysRevLett.91.081301 http://hdl.handle.net/11449/219295 |
identifier_str_mv |
Physical Review Letters, v. 91, n. 8, 2003. 1079-7114 0031-9007 10.1103/PhysRevLett.91.081301 2-s2.0-0141973590 |
dc.language.iso.fl_str_mv |
eng |
language |
eng |
dc.relation.none.fl_str_mv |
Physical Review Letters |
dc.rights.driver.fl_str_mv |
info:eu-repo/semantics/openAccess |
eu_rights_str_mv |
openAccess |
dc.source.none.fl_str_mv |
Scopus reponame:Repositório Institucional da UNESP instname:Universidade Estadual Paulista (UNESP) instacron:UNESP |
instname_str |
Universidade Estadual Paulista (UNESP) |
instacron_str |
UNESP |
institution |
UNESP |
reponame_str |
Repositório Institucional da UNESP |
collection |
Repositório Institucional da UNESP |
repository.name.fl_str_mv |
Repositório Institucional da UNESP - Universidade Estadual Paulista (UNESP) |
repository.mail.fl_str_mv |
|
_version_ |
1808129543777550336 |