1996/08/12 by M. Bordag, K. Kirsten, E. Elizalde +2
Mathematics · Physics and Astronomy · #Boundary (topology) #Boundary value problem #Casimir effect #Classical mechanics #Cosmology and Gravitation Theories #Dirichlet boundary condition #Field (mathematics) #Geometry #Mathematical analysis #Mathematical physics #Mathematics #Noncommutative and Quantum Gravity Theories #Physics #Pure mathematics #Quantum Electrodynamics and Casimir Effect #Quantum mechanics #Renormalization #Scalar (mathematics) #Scalar field #Surface (topology) #Theoretical physics #hep-th
paper · pdf · doi:10.1103/physrevd.56.4896
published as Phys.Rev.D56:4896-4904,1997 · 19 pages, 4 Postscript figures, submitted to Nucl. Phys. B
arxiv created 1996/08/12 · openalex publication_date 1997/10/15 · arxiv updated 2009/11/30 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
The Casimir energy corresponding to a massive scalar field with Dirichlet boundary conditions on a spherical surface is obtained. The field is considered, separately, inside and outside the surface. The renormalization procedure that is necessary to apply in each situation is studied in detail, in particular, the differences occurring with respect to the case when the field occupies the whole space. The final result contains several constants that experience renormalization and can be determined only experimentally. The nontrivial finite parts that appear in the massive case are found exactly, providing a precise determination of the complete, renormalized zero-point energy for the first time.