Induced quantum metric fluctuations and the validity of semiclassical gravity
We propose a criterion for the validity of semiclassical gravity (SCG) which is based on the stability of the solutions of SCG with respect to quantum metric fluctuations. We pay special attention to the two-point quantum correlation functions for the metric perturbations, which contain both intrins...
| Autores: | , , |
|---|---|
| Tipo de documento: | artigo |
| Estado: | Versão publicada |
| Data de publicação: | 2004 |
| País: | España |
| Recursos: | Varias* (Consorci de Biblioteques Universitáries de Catalunya, Centre de Serveis Científics i Acadèmics de Catalunya) |
| Repositório: | Recercat. Dipósit de la Recerca de Catalunya |
| OAI Identifier: | oai:recercat.cat:2445/12375 |
| Acesso em linha: | https://hdl.handle.net/2445/12375 |
| Access Level: | Acceso aberto |
| Palavra-chave: | Gravetat quàntica Teoria quàntica de camps Fluctuacions (Física) Moviment brownià Processos estocàstics Quantum gravity Quantum field theory Fluctuations (Physics) Brownian movements Stochastic processes |
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Induced quantum metric fluctuations and the validity of semiclassical gravityHu, B. L. (Bei-Lok)Roura Crumols, AlbertVerdaguer Oms, Enric, 1950-Gravetat quànticaTeoria quàntica de campsFluctuacions (Física)Moviment browniàProcessos estocàsticsQuantum gravityQuantum field theoryFluctuations (Physics)Brownian movementsStochastic processesWe propose a criterion for the validity of semiclassical gravity (SCG) which is based on the stability of the solutions of SCG with respect to quantum metric fluctuations. We pay special attention to the two-point quantum correlation functions for the metric perturbations, which contain both intrinsic and induced fluctuations. These fluctuations can be described by the Einstein-Langevin equation obtained in the framework of stochastic gravity. Specifically, the Einstein-Langevin equation yields stochastic correlation functions for the metric perturbations which agree, to leading order in the large N limit, with the quantum correlation functions of the theory of gravity interacting with N matter fields. The homogeneous solutions of the Einstein-Langevin equation are equivalent to the solutions of the perturbed semiclassical equation, which describe the evolution of the expectation value of the quantum metric perturbations. The information on the intrinsic fluctuations, which are connected to the initial fluctuations of the metric perturbations, can also be retrieved entirely from the homogeneous solutions. However, the induced metric fluctuations proportional to the noise kernel can only be obtained from the Einstein-Langevin equation (the inhomogeneous term). These equations exhibit runaway solutions with exponential instabilities. A detailed discussion about different methods to deal with these instabilities is given. We illustrate our criterion by showing explicitly that flat space is stable and a description based on SCG is a valid approximation in that case.The American Physical Society201020102004info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersion24 p.application/pdfhttps://hdl.handle.net/2445/12375Articles publicats en revistes (Física de la Matèria Condensada)reponame:Recercat. Dipósit de la Recerca de Catalunyainstname:Varias* (Consorci de Biblioteques Universitáries de Catalunya, Centre de Serveis Científics i Acadèmics de Catalunya)InglésReproducció digital del document publicat en format paper, proporcionada per PROLA i http://dx.doi.org/10.1103/PhysRevD.70.044002Physical Review D, 2004, vol. 70, núm. 4, p. 044002-1-044002-24http://dx.doi.org/10.1103/PhysRevD.70.044002(c) The American Physical Society, 2004info:eu-repo/semantics/openAccessoai:recercat.cat:2445/123752026-05-29T05:05:01Z |
| dc.title.none.fl_str_mv |
Induced quantum metric fluctuations and the validity of semiclassical gravity |
| title |
Induced quantum metric fluctuations and the validity of semiclassical gravity |
| spellingShingle |
Induced quantum metric fluctuations and the validity of semiclassical gravity Hu, B. L. (Bei-Lok) Gravetat quàntica Teoria quàntica de camps Fluctuacions (Física) Moviment brownià Processos estocàstics Quantum gravity Quantum field theory Fluctuations (Physics) Brownian movements Stochastic processes |
| title_short |
Induced quantum metric fluctuations and the validity of semiclassical gravity |
| title_full |
Induced quantum metric fluctuations and the validity of semiclassical gravity |
| title_fullStr |
Induced quantum metric fluctuations and the validity of semiclassical gravity |
| title_full_unstemmed |
Induced quantum metric fluctuations and the validity of semiclassical gravity |
| title_sort |
Induced quantum metric fluctuations and the validity of semiclassical gravity |
| dc.creator.none.fl_str_mv |
Hu, B. L. (Bei-Lok) Roura Crumols, Albert Verdaguer Oms, Enric, 1950- |
| author |
Hu, B. L. (Bei-Lok) |
| author_facet |
Hu, B. L. (Bei-Lok) Roura Crumols, Albert Verdaguer Oms, Enric, 1950- |
| author_role |
author |
| author2 |
Roura Crumols, Albert Verdaguer Oms, Enric, 1950- |
| author2_role |
author author |
| dc.subject.none.fl_str_mv |
Gravetat quàntica Teoria quàntica de camps Fluctuacions (Física) Moviment brownià Processos estocàstics Quantum gravity Quantum field theory Fluctuations (Physics) Brownian movements Stochastic processes |
| topic |
Gravetat quàntica Teoria quàntica de camps Fluctuacions (Física) Moviment brownià Processos estocàstics Quantum gravity Quantum field theory Fluctuations (Physics) Brownian movements Stochastic processes |
| description |
We propose a criterion for the validity of semiclassical gravity (SCG) which is based on the stability of the solutions of SCG with respect to quantum metric fluctuations. We pay special attention to the two-point quantum correlation functions for the metric perturbations, which contain both intrinsic and induced fluctuations. These fluctuations can be described by the Einstein-Langevin equation obtained in the framework of stochastic gravity. Specifically, the Einstein-Langevin equation yields stochastic correlation functions for the metric perturbations which agree, to leading order in the large N limit, with the quantum correlation functions of the theory of gravity interacting with N matter fields. The homogeneous solutions of the Einstein-Langevin equation are equivalent to the solutions of the perturbed semiclassical equation, which describe the evolution of the expectation value of the quantum metric perturbations. The information on the intrinsic fluctuations, which are connected to the initial fluctuations of the metric perturbations, can also be retrieved entirely from the homogeneous solutions. However, the induced metric fluctuations proportional to the noise kernel can only be obtained from the Einstein-Langevin equation (the inhomogeneous term). These equations exhibit runaway solutions with exponential instabilities. A detailed discussion about different methods to deal with these instabilities is given. We illustrate our criterion by showing explicitly that flat space is stable and a description based on SCG is a valid approximation in that case. |
| publishDate |
2004 |
| dc.date.none.fl_str_mv |
2004 2010 2010 |
| dc.type.none.fl_str_mv |
info:eu-repo/semantics/article info:eu-repo/semantics/publishedVersion |
| format |
article |
| status_str |
publishedVersion |
| dc.identifier.none.fl_str_mv |
https://hdl.handle.net/2445/12375 |
| url |
https://hdl.handle.net/2445/12375 |
| dc.language.none.fl_str_mv |
Inglés |
| language_invalid_str_mv |
Inglés |
| dc.relation.none.fl_str_mv |
Reproducció digital del document publicat en format paper, proporcionada per PROLA i http://dx.doi.org/10.1103/PhysRevD.70.044002 Physical Review D, 2004, vol. 70, núm. 4, p. 044002-1-044002-24 http://dx.doi.org/10.1103/PhysRevD.70.044002 |
| dc.rights.none.fl_str_mv |
(c) The American Physical Society, 2004 info:eu-repo/semantics/openAccess |
| rights_invalid_str_mv |
(c) The American Physical Society, 2004 |
| eu_rights_str_mv |
openAccess |
| dc.format.none.fl_str_mv |
24 p. application/pdf |
| dc.publisher.none.fl_str_mv |
The American Physical Society |
| publisher.none.fl_str_mv |
The American Physical Society |
| dc.source.none.fl_str_mv |
Articles publicats en revistes (Física de la Matèria Condensada) reponame:Recercat. Dipósit de la Recerca de Catalunya instname:Varias* (Consorci de Biblioteques Universitáries de Catalunya, Centre de Serveis Científics i Acadèmics de Catalunya) |
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Varias* (Consorci de Biblioteques Universitáries de Catalunya, Centre de Serveis Científics i Acadèmics de Catalunya) |
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Recercat. Dipósit de la Recerca de Catalunya |
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Recercat. Dipósit de la Recerca de Catalunya |
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