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.

arXiv comment21 Pages, 5 Figures

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Cited by in corpus (8)

• Casimir Pistons with General Boundary Conditions
• Spectral Functions for Regular Sturm-Liouville Problems
• Local zeta regularization and the scalar Casimir effect III. The case with a background harmonic potential
• Riemann zeta zeros and zero-point energy
• Some Developments of the Casimir Effect in $p$-Cavity of $(D+1)$-Dimensional Spacetime
• The Casimir effect for pistons with transmittal boundary conditions
• Casimir pistons with generalized boundary conditions: a step forward
• The Casimir Effect for Thick Pistons