2006/07/31 by Inés Cavero-Peláez, Ines Cavero-Pelaez, Kimball A. Milton +1
Mathematics · Physics and Astronomy · #Casimir effect #Classical mechanics #Conformal map #Cosmology and Gravitation Theories #Cylinder #Divergence (linguistics) #Geometry #Mathematical physics #Mathematics #Noncommutative and Quantum Gravity Theories #Physics #Quantum Electrodynamics and Casimir Effect #Quantum electrodynamics #Renormalization #Surface (topology) #hep-th #quant-ph
paper · pdf · doi:10.1088/1751-8113/40/13/019
published as J.Phys.A40:3607-3632,2007 · 28 pages, REVTeX, no figures. Appendix added on perturbative divergences
arxiv created 2006/09/07 · openalex publication_date 2007/03/14 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/06
The local Casimir energy density and the global Casimir energy for a massless scalar field associated with a λδ-function potential in a (3 + 1)-dimensional circular cylindrical geometry are considered. The global energy is examined for both weak and strong coupling, the latter being the well-studied Dirichlet cylinder case. For weak coupling, through , the total energy is shown to vanish by both analytic and numerical arguments, based both on Green's-function and zeta-function techniques. Divergences occurring in the calculation are shown to be absorbable by renormalization of physical parameters of the model. The global energy may be obtained by integrating the local energy density only when the latter is supplemented by an energy term residing precisely on the surface of the cylinder. The latter is identified as the integrated local energy density of the cylindrical shell when the latter is physically expanded to have finite thickness. Inside and outside the δ-function shell, the local energy density diverges as the surface of the shell is approached; the divergence is weakest when the conformal stress tensor is used to define the energy density. A real global divergence first occurs in , as anticipated, but the proof is supplied here for the first time; this divergence is entirely associated with the surface energy and does not reflect divergences in the local energy density as the surface is approached.