Neumann Casimir effect: A singular boundary-interaction approach

Dirichlet boundary conditions on a surface can be imposed on a scalar field, by coupling it quadratically to a δ-like potential, the strength of which tends to infinity. Neumann conditions, on the other hand, require the introduction of an even more singular term, which renders the reflection and tr...

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Autores principales: Fosco, C.D., Lombardo, F.C., Mazzitelli, F.D.
Formato: Artículo publishedVersion
Lenguaje:Inglés
Publicado: 2010
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Acceso en línea:http://hdl.handle.net/20.500.12110/paper_03702693_v690_n2_p189_Fosco
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spelling paperaa:paper_03702693_v690_n2_p189_Fosco2023-06-12T16:47:56Z Neumann Casimir effect: A singular boundary-interaction approach Phys Lett Sect B Nucl Elem Part High-Energy Phys 2010;690(2):189-195 Fosco, C.D. Lombardo, F.C. Mazzitelli, F.D. Boundary conditions Casimir effect Dirichlet boundary conditions on a surface can be imposed on a scalar field, by coupling it quadratically to a δ-like potential, the strength of which tends to infinity. Neumann conditions, on the other hand, require the introduction of an even more singular term, which renders the reflection and transmission coefficients ill-defined because of UV divergences. We present a possible procedure to tame those divergences, by introducing a minimum length scale, related to the nonzero 'width' of a nonlocal term. We then use this setup to reach (either exact or imperfect) Neumann conditions, by taking the appropriate limits. After defining meaningful reflection coefficients, we calculate the Casimir energies for flat parallel mirrors, presenting also the extension of the procedure to the case of arbitrary surfaces. Finally, we discuss briefly how to generalize the worldline approach to the nonlocal case, what is potentially useful in order to compute Casimir energies in theories containing nonlocal potentials; in particular, those which we use to reproduce Neumann boundary conditions. © 2010 Elsevier B.V. All rights reserved. Fil:Lombardo, F.C. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina. Fil:Mazzitelli, F.D. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina. 2010 info:eu-repo/semantics/article info:ar-repo/semantics/artículo info:eu-repo/semantics/publishedVersion application/pdf eng info:eu-repo/semantics/openAccess http://creativecommons.org/licenses/by/2.5/ar http://hdl.handle.net/20.500.12110/paper_03702693_v690_n2_p189_Fosco
institution Universidad de Buenos Aires
institution_str I-28
repository_str R-134
collection Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA)
language Inglés
orig_language_str_mv eng
topic Boundary conditions
Casimir effect
spellingShingle Boundary conditions
Casimir effect
Fosco, C.D.
Lombardo, F.C.
Mazzitelli, F.D.
Neumann Casimir effect: A singular boundary-interaction approach
topic_facet Boundary conditions
Casimir effect
description Dirichlet boundary conditions on a surface can be imposed on a scalar field, by coupling it quadratically to a δ-like potential, the strength of which tends to infinity. Neumann conditions, on the other hand, require the introduction of an even more singular term, which renders the reflection and transmission coefficients ill-defined because of UV divergences. We present a possible procedure to tame those divergences, by introducing a minimum length scale, related to the nonzero 'width' of a nonlocal term. We then use this setup to reach (either exact or imperfect) Neumann conditions, by taking the appropriate limits. After defining meaningful reflection coefficients, we calculate the Casimir energies for flat parallel mirrors, presenting also the extension of the procedure to the case of arbitrary surfaces. Finally, we discuss briefly how to generalize the worldline approach to the nonlocal case, what is potentially useful in order to compute Casimir energies in theories containing nonlocal potentials; in particular, those which we use to reproduce Neumann boundary conditions. © 2010 Elsevier B.V. All rights reserved.
format Artículo
Artículo
publishedVersion
author Fosco, C.D.
Lombardo, F.C.
Mazzitelli, F.D.
author_facet Fosco, C.D.
Lombardo, F.C.
Mazzitelli, F.D.
author_sort Fosco, C.D.
title Neumann Casimir effect: A singular boundary-interaction approach
title_short Neumann Casimir effect: A singular boundary-interaction approach
title_full Neumann Casimir effect: A singular boundary-interaction approach
title_fullStr Neumann Casimir effect: A singular boundary-interaction approach
title_full_unstemmed Neumann Casimir effect: A singular boundary-interaction approach
title_sort neumann casimir effect: a singular boundary-interaction approach
publishDate 2010
url http://hdl.handle.net/20.500.12110/paper_03702693_v690_n2_p189_Fosco
work_keys_str_mv AT foscocd neumanncasimireffectasingularboundaryinteractionapproach
AT lombardofc neumanncasimireffectasingularboundaryinteractionapproach
AT mazzitellifd neumanncasimireffectasingularboundaryinteractionapproach
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