Lifshitz formula for the Casimir force and the GelfandYaglom theorem

We provide a quantum field theory derivation of the Lifshitz formula for the Casimir force due to a fluctuating real scalar field in d + 1 dimensions. The field is coupled to two imperfect, thick, plane mirrors, which are modeled by background potentials localized on their positions. The derivation...

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Detalles Bibliográficos
Autor principal: Mazzitelli, Francisco Diego
Publicado: 2011
Acceso en línea:https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_17518113_v44_n46_p_Ttira
http://hdl.handle.net/20.500.12110/paper_17518113_v44_n46_p_Ttira
Aporte de:
Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA) de Universidad de Buenos Aires
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spelling paper:paper_17518113_v44_n46_p_Ttira2023-06-08T16:28:43Z Lifshitz formula for the Casimir force and the GelfandYaglom theorem Mazzitelli, Francisco Diego We provide a quantum field theory derivation of the Lifshitz formula for the Casimir force due to a fluctuating real scalar field in d + 1 dimensions. The field is coupled to two imperfect, thick, plane mirrors, which are modeled by background potentials localized on their positions. The derivation proceeds from the calculation of the vacuum energy in the Euclidean version of the system, reducing the problem to the evaluation of a functional determinant. The latter is written, via Gelfand-Yagloms formula, in terms of functions depending on the structure of the potential describing each mirror; those functions encode the properties which are relevant to the Casimir force and are the reflection coefficients evaluated at imaginary frequencies. © 2011 IOP Publishing Ltd. Fil:Mazzitelli, F.D. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina. 2011 https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_17518113_v44_n46_p_Ttira http://hdl.handle.net/20.500.12110/paper_17518113_v44_n46_p_Ttira
institution Universidad de Buenos Aires
institution_str I-28
repository_str R-134
collection Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA)
description We provide a quantum field theory derivation of the Lifshitz formula for the Casimir force due to a fluctuating real scalar field in d + 1 dimensions. The field is coupled to two imperfect, thick, plane mirrors, which are modeled by background potentials localized on their positions. The derivation proceeds from the calculation of the vacuum energy in the Euclidean version of the system, reducing the problem to the evaluation of a functional determinant. The latter is written, via Gelfand-Yagloms formula, in terms of functions depending on the structure of the potential describing each mirror; those functions encode the properties which are relevant to the Casimir force and are the reflection coefficients evaluated at imaginary frequencies. © 2011 IOP Publishing Ltd.
author Mazzitelli, Francisco Diego
spellingShingle Mazzitelli, Francisco Diego
Lifshitz formula for the Casimir force and the GelfandYaglom theorem
author_facet Mazzitelli, Francisco Diego
author_sort Mazzitelli, Francisco Diego
title Lifshitz formula for the Casimir force and the GelfandYaglom theorem
title_short Lifshitz formula for the Casimir force and the GelfandYaglom theorem
title_full Lifshitz formula for the Casimir force and the GelfandYaglom theorem
title_fullStr Lifshitz formula for the Casimir force and the GelfandYaglom theorem
title_full_unstemmed Lifshitz formula for the Casimir force and the GelfandYaglom theorem
title_sort lifshitz formula for the casimir force and the gelfandyaglom theorem
publishDate 2011
url https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_17518113_v44_n46_p_Ttira
http://hdl.handle.net/20.500.12110/paper_17518113_v44_n46_p_Ttira
work_keys_str_mv AT mazzitellifranciscodiego lifshitzformulaforthecasimirforceandthegelfandyaglomtheorem
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