A Global Approach with Cutoff Exponential Function, Mathematically Well Defined at the Outset, for Calculating the Casimir Energy: The Example of Scalar FieldReportar como inadecuado




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Advances in High Energy PhysicsVolume 2010 2010, Article ID 120964, 13 pages

Research ArticleDepartamento de Física-UEFS, 44036-900 Feira de Santana, BA, Brazil

Received 9 October 2010; Accepted 6 December 2010

Academic Editor: Ira Rothstein

Copyright © 2010 M. S. R. Miltão and Franz A. Farias. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

A global approach with cutoff exponential functions is used to obtain the Casimir energy of a masslessscalar field in the presence of a spherical shell. The proposed method, mathematically well defined at theoutset, makes use of two regulators, one of them to make the sum of the orders of Bessel functions finiteand the other to regularize the integral involving the zeros of Bessel function. This procedure ensures aconsistent mathematical handling in the calculations of the Casimir energy and allows a major comprehensionon the regularization process when nontrivial symmetries are under consideration. In particular, we determinethe Casimir energy of a scalar field, showing all kinds of divergences. We consider separately the contributions of the inner and outer regions of a spherical shell and show that the results obtained are in agreement withthose known in the literature, and this gives a confirmation for the consistence of the proposed approach. Thechoice of the scalar field was due to its simplicity in terms of physical quantity spin.





Autor: M. S. R. Miltão and Franz A. Farias

Fuente: https://www.hindawi.com/



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