The Casimir effect for parallel plates revisited

Journal Article · Mon Oct 15 04:00:00 EDT 2007 · Journal of Mathematical Physics

DOI:https://doi.org/10.1063/1.2794562· OSTI ID:21013731

Kawakami, N A; Nemes, M C; Wreszinski, Walter F ^[1]

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1. Departamento de Fisica, Instituto de Ciencias Exatas, Universidade Federal de Minas Gerais, Caixa Postal 970, Belo Horizonte, CEP 30161-970 Minas Gerais (Brazil)

The Casimir effect for a massless scalar field with Dirichlet and periodic boundary conditions (bc's) on infinite parallel plates is revisited in the local quantum field theory (lqft) framework introduced by Kay [Phys. Rev. D 20, 3052 (1979)]. The model displays a number of more realistic features than the ones he treated. In addition to local observables, as the energy density, we propose to consider intensive variables, such as the energy per unit area {epsilon}, as fundamental observables. Adopting this view, lqft rejects Dirichlet (the same result may be proved for Neumann or mixed) bc, and accepts periodic bc: in the former case {epsilon} diverges, in the latter it is finite, as is shown by an expression for the local energy density obtained from lqft through the use of the Poisson summation formula. Another way to see this uses methods from the Euler summation formula: in the proof of regularization independence of the energy per unit area, a regularization-dependent surface term arises upon use of Dirichlet bc, but not periodic bc. For the conformally invariant scalar quantum field, this surface term is absent due to the condition of zero trace of the energy momentum tensor, as remarked by De Witt [Phys. Rep. 19, 295 (1975)]. The latter property does not hold in the application to the dark energy problem in cosmology, in which we argue that periodic bc might play a distinguished role.

• OSTI ID: 21013731
• Journal Information: Journal of Mathematical Physics, Journal Name: Journal of Mathematical Physics Journal Issue: 10 Vol. 48; ISSN JMAPAQ; ISSN 0022-2488
• Country of Publication: United States
• Language: English

Related Subjects

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
BOUNDARY CONDITIONS
BOUNDARY-VALUE PROBLEMS
CASIMIR EFFECT
CONFORMAL INVARIANCE
COSMOLOGY
ENERGY DENSITY
ENERGY-MOMENTUM TENSOR
NONLUMINOUS MATTER
PERIODICITY
QUANTUM FIELD THEORY
RENORMALIZATION
SCALAR FIELDS