2005/09/30 by Martin Schaden
Mathematics · Physics and Astronomy · #Boundary value problem #Casimir effect #Cosmology and Gravitation Theories #Geometry #Manifold (fluid mechanics) #Massless particle #Mathematical analysis #Mathematical physics #Mathematics #Noncommutative and Quantum Gravity Theories #Physics #Quantum #Quantum Electrodynamics and Casimir Effect #Quantum electrodynamics #Quantum mechanics #Regularization (linguistics) #Riemann zeta function #Scalar (mathematics) #Scalar field #Semiclassical physics #Sign (mathematics) #Zeta function regularization #hep-th
paper · pdf · doi:10.1103/physreva.73.042102
published as Phys.Rev.A73:042102,2006 · 39 pages, no figures, references added, some corrections
arxiv created 2005/10/27 · openalex publication_date 2006/04/07 · arxiv updated 2009/12/01 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
The Casimir energy of a massless scalar field is semiclassically given by contributions due to classical periodic rays. The required subtractions in the spectral density are determined explicitly. The semiclassical Casimir energies so defined coincide with those of zeta function regularization in the cases studied. Poles in the analytic continuation of zeta function regularization are related to nonuniversal subtractions in the spectral density. The sign of the Casimir energy of a scalar field on a smooth manifold is estimated by the sign of the contribution due to the shortest periodic rays only. Demanding continuity of the Casimir energy under small deformations of the manifold, the method is extended to integrable systems. The Casimir energy of a massless scalar field on a manifold with boundaries includes contributions due to periodic rays that lie entirely within the boundaries. These contributions in general depend on the boundary conditions. Although the Casimir energy due to a massless scalar field may be sensitive to the physical dimensions of manifolds with boundary. In favorable cases its sign can, contrary to conventional wisdom, be inferred without calculation of the Casimir energy.