On the non-relativistic Casimir effect

Detalhes bibliográficos
Autor(a) principal: Cougo-Pinto,M.V.
Data de Publicação: 2001
Outros Autores: Farina,C., Mendes,J.F.M., Tort,A.C.
Tipo de documento: Artigo
Idioma: eng
Título da fonte: Brazilian Journal of Physics
Texto Completo: http://old.scielo.br/scielo.php?script=sci_arttext&pid=S0103-97332001000100008
Resumo: We compute the Casimir energy for a massive scalar field constrained between two parallel planes (Dirichlet boundary conditions) in order to investigate its non-relativistic limit. Instead of employing the usual relativistic dispersion relation omega(p) = <img SRC="http:/img/fbpe/bjp/v31n1/08eq01.gif">, we use the non-relativistic one, omega(p) = p²/2m. It turns out that the Casimir energy is zero. We include the relativistic corrections perturbatively and show that at all orders the Casimir energy remains zero, since each term in the power series in 1/c² is proportional to the Riemann zeta function of a negative even integer. This puzzling result shows that, at least for the free massive scalar field, the Casimir effect is non-perturbative in the relativistic sense.
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spelling On the non-relativistic Casimir effectWe compute the Casimir energy for a massive scalar field constrained between two parallel planes (Dirichlet boundary conditions) in order to investigate its non-relativistic limit. Instead of employing the usual relativistic dispersion relation omega(p) = <img SRC="http:/img/fbpe/bjp/v31n1/08eq01.gif">, we use the non-relativistic one, omega(p) = p²/2m. It turns out that the Casimir energy is zero. We include the relativistic corrections perturbatively and show that at all orders the Casimir energy remains zero, since each term in the power series in 1/c² is proportional to the Riemann zeta function of a negative even integer. This puzzling result shows that, at least for the free massive scalar field, the Casimir effect is non-perturbative in the relativistic sense.Sociedade Brasileira de Física2001-03-01info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersiontext/htmlhttp://old.scielo.br/scielo.php?script=sci_arttext&pid=S0103-97332001000100008Brazilian Journal of Physics v.31 n.1 2001reponame:Brazilian Journal of Physicsinstname:Sociedade Brasileira de Física (SBF)instacron:SBF10.1590/S0103-97332001000100008info:eu-repo/semantics/openAccessCougo-Pinto,M.V.Farina,C.Mendes,J.F.M.Tort,A.C.eng2002-02-18T00:00:00Zoai:scielo:S0103-97332001000100008Revistahttp://www.sbfisica.org.br/v1/home/index.php/pt/ONGhttps://old.scielo.br/oai/scielo-oai.phpsbfisica@sbfisica.org.br||sbfisica@sbfisica.org.br1678-44480103-9733opendoar:2002-02-18T00:00Brazilian Journal of Physics - Sociedade Brasileira de Física (SBF)false
dc.title.none.fl_str_mv On the non-relativistic Casimir effect
title On the non-relativistic Casimir effect
spellingShingle On the non-relativistic Casimir effect
Cougo-Pinto,M.V.
title_short On the non-relativistic Casimir effect
title_full On the non-relativistic Casimir effect
title_fullStr On the non-relativistic Casimir effect
title_full_unstemmed On the non-relativistic Casimir effect
title_sort On the non-relativistic Casimir effect
author Cougo-Pinto,M.V.
author_facet Cougo-Pinto,M.V.
Farina,C.
Mendes,J.F.M.
Tort,A.C.
author_role author
author2 Farina,C.
Mendes,J.F.M.
Tort,A.C.
author2_role author
author
author
dc.contributor.author.fl_str_mv Cougo-Pinto,M.V.
Farina,C.
Mendes,J.F.M.
Tort,A.C.
description We compute the Casimir energy for a massive scalar field constrained between two parallel planes (Dirichlet boundary conditions) in order to investigate its non-relativistic limit. Instead of employing the usual relativistic dispersion relation omega(p) = <img SRC="http:/img/fbpe/bjp/v31n1/08eq01.gif">, we use the non-relativistic one, omega(p) = p²/2m. It turns out that the Casimir energy is zero. We include the relativistic corrections perturbatively and show that at all orders the Casimir energy remains zero, since each term in the power series in 1/c² is proportional to the Riemann zeta function of a negative even integer. This puzzling result shows that, at least for the free massive scalar field, the Casimir effect is non-perturbative in the relativistic sense.
publishDate 2001
dc.date.none.fl_str_mv 2001-03-01
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=S0103-97332001000100008
url http://old.scielo.br/scielo.php?script=sci_arttext&pid=S0103-97332001000100008
dc.language.iso.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv 10.1590/S0103-97332001000100008
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 Brazilian Journal of Physics v.31 n.1 2001
reponame:Brazilian Journal of Physics
instname:Sociedade Brasileira de Física (SBF)
instacron:SBF
instname_str Sociedade Brasileira de Física (SBF)
instacron_str SBF
institution SBF
reponame_str Brazilian Journal of Physics
collection Brazilian Journal of Physics
repository.name.fl_str_mv Brazilian Journal of Physics - Sociedade Brasileira de Física (SBF)
repository.mail.fl_str_mv sbfisica@sbfisica.org.br||sbfisica@sbfisica.org.br
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