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Many-body contributions to Green’s functions and Casimir energies

K. V. Shajesh* and M. Schaden†

  • Department of Physics, Rutgers, The State University of New Jersey, 101 Warren Street, Newark, New Jersey 07102, USA

  • *shajesh@andromeda.rutgers.edu; http://andromeda.rutgers.edu/~shajesh
  • †mschaden@andromeda.rutgers.edu; http://andromeda.rutgers.edu/~physics/mschaden.htm
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Phys. Rev. D 83, 125032 – Published 29 June, 2011

DOI: https://doi.org/10.1103/PhysRevD.83.125032

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.

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Phys. Rev. D 83, 125032– Published 29 June, 2011
  • Received 15 March 2011
Article part of CHORUS

© 2011 American Physical Society

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