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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Acceso en línea: | http://hdl.handle.net/20.500.12110/paper_03702693_v690_n2_p189_Fosco |
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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 |
_version_ |
1769810289116577792 |