On the non-relativistic Casimir effect

On the non-relativistic Casimir effect

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.

Saved in:
Bibliographic Details
Main Authors: Cougo-Pinto,M.V., Farina,C., Mendes,J.F.M., Tort,A.C.
Format: Digital revista
Language:English
Published: Sociedade Brasileira de Física 2001
Online Access:http://old.scielo.br/scielo.php?script=sci_arttext&pid=S0103-97332001000100008
Tags: Add Tag
No Tags, Be the first to tag this record!
id oai:scielo:S0103-97332001000100008
record_format ojs
spelling oai:scielo:S0103-973320010001000082002-02-18On the non-relativistic Casimir effectCougo-Pinto,M.V.Farina,C.Mendes,J.F.M.Tort,A.C.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.info:eu-repo/semantics/openAccessSociedade Brasileira de FísicaBrazilian Journal of Physics v.31 n.1 20012001-03-01info:eu-repo/semantics/articletext/htmlhttp://old.scielo.br/scielo.php?script=sci_arttext&pid=S0103-97332001000100008en10.1590/S0103-97332001000100008
institution SCIELO
collection OJS
country Brasil
countrycode BR
component Revista
access En linea
databasecode rev-scielo-br
tag revista
region America del Sur
libraryname SciELO
language English
format Digital
author Cougo-Pinto,M.V.
Farina,C.
Mendes,J.F.M.
Tort,A.C.
spellingShingle Cougo-Pinto,M.V.
Farina,C.
Mendes,J.F.M.
Tort,A.C.
On the non-relativistic Casimir effect
author_facet Cougo-Pinto,M.V.
Farina,C.
Mendes,J.F.M.
Tort,A.C.
author_sort Cougo-Pinto,M.V.
title On the non-relativistic Casimir effect
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
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.
publisher Sociedade Brasileira de Física
publishDate 2001
url http://old.scielo.br/scielo.php?script=sci_arttext&pid=S0103-97332001000100008
work_keys_str_mv AT cougopintomv onthenonrelativisticcasimireffect
AT farinac onthenonrelativisticcasimireffect
AT mendesjfm onthenonrelativisticcasimireffect
AT tortac onthenonrelativisticcasimireffect
_version_ 1756407232813072384

Similar Items