Many-Body Contributions to Green's Functions and Casimir Energies

Abstract

The multiple scattering formalism is used to extract irreducible N-body parts of Green's functions and Casimir energies describing the interaction of N objects that are not necessarily mutually disjoint. The irreducible N-body scattering matrix is expressed in terms of single-body transition matrices. The irreducible N-body Casimir energy is the trace of the corresponding irreducible N-body part of the Green's function. This formalism requires the solution of a set of linear integral equations. The irreducible three-body Green's function and the corresponding Casimir energy of a massless scalar field interacting with potentials are obtained and evaluated for three parallel semitransparent plates. When Dirichlet boundary conditions are imposed on a plate the Green's function and Casimir energy decouple into contributions from two disjoint regions. We also consider weakly interacting triangular--and parabolic-wedges placed atop a Dirichlet plate. The irreducible three-body Casimir energy of a triangular--and parabolic-wedge is minimal when the shorter side of the wedge is perpendicular to the Dirichlet plate. The irreducible three-body contribution to the vacuum energy is finite and positive in all the cases studied.

22 pages, 8 figures

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• Casimir energy of $N$ magnetodielectric $\delta$-function plates
• Quantum Vacuum Energy of Self-Similar Configurations
• Significance of many-body contributions to Casimir energies
• Irreducible Scalar Many-Body Casimir Energies: Theorems and Numerical Studies
• Geometrical dependence in Casimir-Polder repulsion: Anisotropically polarizable atom and anisotropically polarizable annular dielectric
• Quasiperiodic arrangement of magnetodielectric $\delta$-plates: Green's functions and Casimir energies for $N$ bodies
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