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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Detalles Bibliográficos
Autores principales: Lombardo, Fernando César, Mazzitelli, Francisco Diego
Publicado: 2010
Materias:
Boundary conditions
Casimir effect
Acceso en línea:https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_03702693_v690_n2_p189_Fosco
http://hdl.handle.net/20.500.12110/paper_03702693_v690_n2_p189_Fosco
Aporte de:
Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA) de Universidad de Buenos Aires
id paper:paper_03702693_v690_n2_p189_Fosco
record_format dspace
spelling paper:paper_03702693_v690_n2_p189_Fosco2023-06-08T15:36:50Z Neumann Casimir effect: A singular boundary-interaction approach Lombardo, Fernando César Mazzitelli, Francisco Diego 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 https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_03702693_v690_n2_p189_Fosco 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)
topic Boundary conditions
Casimir effect
spellingShingle Boundary conditions
Casimir effect
Lombardo, Fernando César
Mazzitelli, Francisco Diego
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.
author Lombardo, Fernando César
Mazzitelli, Francisco Diego
author_facet Lombardo, Fernando César
Mazzitelli, Francisco Diego
author_sort Lombardo, Fernando César
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 https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_03702693_v690_n2_p189_Fosco
http://hdl.handle.net/20.500.12110/paper_03702693_v690_n2_p189_Fosco
work_keys_str_mv AT lombardofernandocesar neumanncasimireffectasingularboundaryinteractionapproach
AT mazzitellifranciscodiego neumanncasimireffectasingularboundaryinteractionapproach
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