Irreducible many-body Casimir energies of intersecting objects

Department of Physics, Rutgers University - 101 Warren Street, Newark, NJ 07102, USA

^a mschaden@rutgers.edu

Received: 14 February 2011
Accepted: 4 April 2011

Abstract

The vacuum energy of bosonic fields interacting locally with objects is decomposed into irreducible many-body parts. The irreducible N-body contribution is finite if the N objects have no common intersection, O₁∩O₂···∩ O_N=∅. The perturbative high-temperature expansion of the corresponding irreducible N-body spectral function vanishes to all orders even if some of the objects overlap. These irreducible spectral functions and their associated Casimir energies can, in principle, be computed numerically or approximated semi-classically without regularization or implicit knowledge of the spectrum. They are analytic in the parameters describing the relative orientation and position of the individual objects and remain finite when some, but not all, of the N objects overlap. The finiteness of the irreducible N-body Casimir energy of a massless scalar field with potential scattering is explicitly verified and found to be negative for an even, and positive for an odd number of objects. The sign in this case does not depend on the strength of the local N-body potentials. Some simple examples illustrate the analyticity of N-body Casimir energies. A multiple scattering representation of the irreducible three-body Casimir energy is derived. It remains finite when the three objects overlap only pairwise.