Casimir effect for the scalar field under Robin boundary conditions: A functional integral approach

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dc.creatorde Albuquerque, Luiz C.
dc.creatorCavalcanti, R. M.
dc.date2003-11-06
dc.date2004-06-01
dc.date.accessioned2026-07-07T04:16:07Z
dc.date.available2026-07-07T04:16:07Z
dc.descriptionIn this work we show how to define the action of a scalar field in a such a way that Robin boundary condition is implemented dynamically, i.e., as a consequence of the stationary action principle. We discuss the quantization of that system via functional integration. Using this formalism, we derive an expression for the Casimir energy of a massless scalar field under Robin boundary conditions on a pair of parallel plates, characterized by constants $c_1$ and $c_2$. Some special cases are discussed; in particular, we show that for some values of $c_1$ and $c_2$ the Casimir energy as a function of the distance between the plates presents a minimum. We also discuss the renormalization at one-loop order of the two-point Green function in the $λϕ^4$ theory submitted to Robin boundary condition on a plate.
dc.description16 pages, 2 figures. Version 2: contains a new section on the renormalization of the two-point Green function in the presence of a flat boundary. Accepted for publication in J. Phys. A
dc.identifierhttps://arxiv.org/abs/hep-th/0311052
dc.identifierhttp://arxiv.org/abs/hep-th/0311052
dc.identifierJ.Phys. A37 (2004) 7039-7050
dc.identifierdoi:10.1088/0305-4470/37/27/012
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/52223
dc.subjectHigh Energy Physics - Theory
dc.titleCasimir effect for the scalar field under Robin boundary conditions: A functional integral approach
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