Casimir effect in the presence of external fields

Abstract

In this work the Casimir effect is studied for scalar fields in the presence of boundaries and under the influence of arbitrary smooth potentials of compact support. In this setting, piston configurations are analyzed in which the piston is modeled by a potential. For these configurations, analytic results for the Casimir energy and force are obtained by employing the zeta function regularization method. Also, explicit numerical results for the Casimir force are provided for pistons modeled by a class of compactly supported potentials that are realizable as delta-sequences. These results are then generalized to higher dimensional pistons by considering additional Kaluza-Klein dimensions.

Local zeta regularization and the scalar Casimir effect III. The case with a background harmonic potential

“…(3.24) in u = 0 in the case of odd d implies the appearance of a logarithmic term in τ in the integrand ( 4 ). Simple but rather lenghty computations give the following 3 As a matter of fact, for computational simplicity, we will always choose the smaller n ∈ {0, 1, 2, ...} fulfilling Eq. (3.26).…”

The Casimir effect for thick pistons

“…An attempt at addressing the first problem can be found for instance in [21] where the Casimir effect is studied for a piston configuration endowed with general boundary conditions. A different approach was undertaken in [1,3,17,19] where the ideal boundary conditions were replaced by a suitable potential function which would better describe the physical properties of real materials. The Casimir effect for materials of finite thickness, instead, has been analyzed within the framework of piston configurations for instance in [2,36].…”

Casimir pistons with general boundary conditions

“…It is important to mention, for completeness, that real materials could be modeled by smooth potentials with compact support rather than boundaries (see e.g. [1,5,27,26,19]).…”