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: Fosco, C.D., Lombardo, F.C., Mazzitelli, F.D.
Formato: Artículo publishedVersion
Publicado: 2010
Materias:
Acceso en línea: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 Ver origen
Descripción
Sumario: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.