Casimir effect with nonlocal boundary interactions

Abstract

We derive a general expression for the Casimir energy corresponding to two flat parallel mirrors in d+1 dimensions, described by nonlocal interaction potentials. For a real scalar field, the interaction with the mirrors is implemented by a term which is a quadratic form in the field, with a nonlocal kernel. The resulting expression for the energy is a function of the parameters that define the nonlocal kernel. We show that the general expression has the correct limit in the zero width case, and also present the exact solution for a particular case.

13 pages, LaTeX; minor misprints corrected

References in corpus (7)

• The Casimir effect: Recent controversies and progress
• Casimir forces in a T operator approach
• Multiple Scattering Methods in Casimir Calculations
• Spatial dispersion in Casimir forces: A brief review
• Casimir effect with dynamical matter on thin mirrors
• Casimir energies with finite-width mirrors
• Casimir effect with non-local boundary conditions

Cited by in corpus (3)

• Derivative expansion for the boundary interaction terms in the Casimir effect: generalized $\delta$-potentials
• Global vs local Casimir effect
• Vacuum fluctuations in the presence of nonlinear boundary conditions