Neumann Casimir effect: A singular boundary-interaction approach

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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
Publicado:	2010
Materias:	Boundary conditions Casimir effect
Acceso en línea:	http://hdl.handle.net/20.500.12110/paper_03702693_v690_n2_p189_Fosco https://repositoriouba.sisbi.uba.ar/gsdl/cgi-bin/library.cgi?a=d&c=artiaex&d=paper_03702693_v690_n2_p189_Fosco_oai
Aporte de:	Repositorio Digital de la Universidad de Buenos Aires (UBA) de Universidad de Buenos Aires

id	I28-R145-paper_03702693_v690_n2_p189_Fosco_oai
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spelling	I28-R145-paper_03702693_v690_n2_p189_Fosco_oai2024-08-16 Fosco, C.D. Lombardo, F.C. Mazzitelli, F.D. 2010 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. application/pdf http://hdl.handle.net/20.500.12110/paper_03702693_v690_n2_p189_Fosco info:eu-repo/semantics/openAccess http://creativecommons.org/licenses/by/2.5/ar Phys Lett Sect B Nucl Elem Part High-Energy Phys 2010;690(2):189-195 Boundary conditions Casimir effect Neumann Casimir effect: A singular boundary-interaction approach info:eu-repo/semantics/article info:ar-repo/semantics/artículo info:eu-repo/semantics/publishedVersion https://repositoriouba.sisbi.uba.ar/gsdl/cgi-bin/library.cgi?a=d&c=artiaex&d=paper_03702693_v690_n2_p189_Fosco_oai
institution	Universidad de Buenos Aires
institution_str	I-28
repository_str	R-145
collection	Repositorio Digital de la Universidad de Buenos Aires (UBA)
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 https://repositoriouba.sisbi.uba.ar/gsdl/cgi-bin/library.cgi?a=d&c=artiaex&d=paper_03702693_v690_n2_p189_Fosco_oai
work_keys_str_mv	AT foscocd neumanncasimireffectasingularboundaryinteractionapproach AT lombardofc neumanncasimireffectasingularboundaryinteractionapproach AT mazzitellifd neumanncasimireffectasingularboundaryinteractionapproach
_version_	1809357099495325696

Neumann Casimir effect: A singular boundary-interaction approach

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