Casimir energy for the scalar field: a global approach with cut-off exponential function

Abstract

A global approach with cut-off exponential functions previously proposed is used to obtain the Casimir energy of a massless scalar field in the presence of a spherical shell. The proposed method makes the use of two regulators, one of them to makes finite the sum of the orders of Bessel functions and the other, to regularizes the integral involving the zeros of Bessel function. This procedure ensures a consistent mathematical handling in the calculations of the Casimir energy for a scalar field and allows to show all types 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 with those known in the literature and this gives a confirmation for the consistence of the proposed approach.

7 pages, 2 figures, abstract revised, equations revised, references added and minor corrections

References in corpus (9)

• The Casimir effect: Recent controversies and progress
• Casimir forces between arbitrary compact objects
• The generalized Abel-Plana formula with applications to Bessel functions and Casimir effect
• Casimir force for a scalar field in warped brane worlds
• Energy-momentum tensor of a Casimir apparatus in a weak gravitational field: scalar case
• Energy-momentum tensor for a scalar Casimir apparatus in a weak gravitational field: Neumann conditions
• An extension of the Linear Delta Expansion to Superspace
• Dynamical Casimir effect for a massless scalar field between two concentric spherical shells
• Casimir effect at finite temperature in a real scalar field theory