The Casimir spectrum revisited
Autor(a) principal: | |
---|---|
Data de Publicação: | 2011 |
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/10773/7080 |
Resumo: | We examine the mathematical and physical significance of the spectral density sigma(omega) introduced by Ford [Phys. Rev. D 38, 528 (1988)], defining the contribution of each frequency to the renormalised energy density of a quantum field. Firstly, by considering a simple example, we argue that sigma(omega) is well defined, in the sense of being regulator independent, despite an apparently regulator dependent definition. We then suggest that sigma(omega) is a spectral distribution, rather than a function, which only produces physically meaningful results when integrated over a sufficiently large range of frequencies and with a high energy smooth enough regulator. Moreover, sigma(omega) is seen to be simply the difference between the bare spectral density and the spectral density of the reference background. This interpretation yields a simple "rule of thumb" to writing down a (formal) expression for sigma(omega) as shown in an explicit example. Finally, by considering an example in which the sign of the Casimir force varies, we show that the spectrum carries no manifest information about this sign; it can only be inferred by integrating sigma(omega). (C) 2011 American Institute of Physics. [doi:10.1063/1.3614003] |
id |
RCAP_f69307ffb46aad0a0f0158bd61e49f26 |
---|---|
oai_identifier_str |
oai:ria.ua.pt:10773/7080 |
network_acronym_str |
RCAP |
network_name_str |
Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) |
repository_id_str |
7160 |
spelling |
The Casimir spectrum revisitedWe examine the mathematical and physical significance of the spectral density sigma(omega) introduced by Ford [Phys. Rev. D 38, 528 (1988)], defining the contribution of each frequency to the renormalised energy density of a quantum field. Firstly, by considering a simple example, we argue that sigma(omega) is well defined, in the sense of being regulator independent, despite an apparently regulator dependent definition. We then suggest that sigma(omega) is a spectral distribution, rather than a function, which only produces physically meaningful results when integrated over a sufficiently large range of frequencies and with a high energy smooth enough regulator. Moreover, sigma(omega) is seen to be simply the difference between the bare spectral density and the spectral density of the reference background. This interpretation yields a simple "rule of thumb" to writing down a (formal) expression for sigma(omega) as shown in an explicit example. Finally, by considering an example in which the sign of the Casimir force varies, we show that the spectrum carries no manifest information about this sign; it can only be inferred by integrating sigma(omega). (C) 2011 American Institute of Physics. [doi:10.1063/1.3614003]American Institute of Physics2012-02-29T15:16:57Z2011-01-01T00:00:00Z2011info:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/articleapplication/pdfhttp://hdl.handle.net/10773/7080eng0022-248810.1063/1.3614003Herdeiro, Carlos A. R.Sampaio, Marco O. P.Santos, Jaime E.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:RCAAP2024-02-22T11:11:08Zoai:ria.ua.pt:10773/7080Portal AgregadorONGhttps://www.rcaap.pt/oai/openaireopendoar:71602024-03-20T02:44:32.401246Repositório 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 |
The Casimir spectrum revisited |
title |
The Casimir spectrum revisited |
spellingShingle |
The Casimir spectrum revisited Herdeiro, Carlos A. R. |
title_short |
The Casimir spectrum revisited |
title_full |
The Casimir spectrum revisited |
title_fullStr |
The Casimir spectrum revisited |
title_full_unstemmed |
The Casimir spectrum revisited |
title_sort |
The Casimir spectrum revisited |
author |
Herdeiro, Carlos A. R. |
author_facet |
Herdeiro, Carlos A. R. Sampaio, Marco O. P. Santos, Jaime E. |
author_role |
author |
author2 |
Sampaio, Marco O. P. Santos, Jaime E. |
author2_role |
author author |
dc.contributor.author.fl_str_mv |
Herdeiro, Carlos A. R. Sampaio, Marco O. P. Santos, Jaime E. |
description |
We examine the mathematical and physical significance of the spectral density sigma(omega) introduced by Ford [Phys. Rev. D 38, 528 (1988)], defining the contribution of each frequency to the renormalised energy density of a quantum field. Firstly, by considering a simple example, we argue that sigma(omega) is well defined, in the sense of being regulator independent, despite an apparently regulator dependent definition. We then suggest that sigma(omega) is a spectral distribution, rather than a function, which only produces physically meaningful results when integrated over a sufficiently large range of frequencies and with a high energy smooth enough regulator. Moreover, sigma(omega) is seen to be simply the difference between the bare spectral density and the spectral density of the reference background. This interpretation yields a simple "rule of thumb" to writing down a (formal) expression for sigma(omega) as shown in an explicit example. Finally, by considering an example in which the sign of the Casimir force varies, we show that the spectrum carries no manifest information about this sign; it can only be inferred by integrating sigma(omega). (C) 2011 American Institute of Physics. [doi:10.1063/1.3614003] |
publishDate |
2011 |
dc.date.none.fl_str_mv |
2011-01-01T00:00:00Z 2011 2012-02-29T15:16:57Z |
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/10773/7080 |
url |
http://hdl.handle.net/10773/7080 |
dc.language.iso.fl_str_mv |
eng |
language |
eng |
dc.relation.none.fl_str_mv |
0022-2488 10.1063/1.3614003 |
dc.rights.driver.fl_str_mv |
info:eu-repo/semantics/openAccess |
eu_rights_str_mv |
openAccess |
dc.format.none.fl_str_mv |
application/pdf |
dc.publisher.none.fl_str_mv |
American Institute of Physics |
publisher.none.fl_str_mv |
American Institute of Physics |
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 |
|
_version_ |
1799137496528846848 |