Casimir self-energy of a δ-δ' sphere

Abstract

We extend previous work on the vacuum energy of a massless scalar field in the presence of singular potentials. We consider a single sphere denoted by the so-called "delta-delta prime" interaction. Contrary to the Dirac delta potential, we find a nontrivial one-parameter family of potentials such that the regularization procedure gives an unambiguous result for the Casimir self-energy. The procedure employed is based on the zeta function regularization and the cancellation of the heat kernel coefficient a_2. The results obtained are in agreement with particular cases, such as the Dirac delta or Robin and Dirichlet boundary conditions.

References in corpus (26)

• Heat kernel expansion: user's manual
• The Casimir effect: Recent controversies and progress
• Scattering Theory Approach to Electrodynamic Casimir Forces
• Opposites Attract - A Theorem About The Casimir Force
• Casimir forces in a T operator approach
• On the ground state energy for a penetrable sphere and for a dielectric ball
• Global Theory of Quantum Boundary Conditions and Topology Change
• Identity of the van der Waals Force and the Casimir Effect and the Irrelevance of these Phenomena to Sonoluminescence
• Mode-by-mode summation for the zero point electromagnetic energy of an infinite cylinder
• Complete zeta-function approach to the electromagnetic Casimir effect for spheres and circles
• Heat Kernel Expansion for Semitransparent Boundaries
• Casimir Energies and Pressures for $\delta$-function Potentials
• Vacuum energy in a spherically symmetric background field
• Casimir Energy for a Spherical Cavity in a Dielectric: Applications to Sonoluminescence
• Casimir's energy of a conducting sphere and of a dilute dielectric ball
• Casimir Energy for a Purely Dielectric Cylinder by the Mode Summation Method
• Casimir Energy for a Dielectric Cylinder
• $\delta -{\delta }^{\prime }$ generalized Robin boundary conditions and quantum vacuum fluctuations
• Non-contact gears: I. Next-to-leading order contribution to lateral Casimir force between corrugated parallel plates
• Casimir energy and dilute dielectric ball
• Local Casimir Energies for a Thin Spherical Shell
• Casimir forces in inhomogeneous media: renormalization and the principle of virtual work
• The Topology and Geometry of self-adjoint and elliptic boundary conditions for Dirac and Laplace operators
• An approximation to the Woods-Saxon potential based on a contact interaction
• Casimir Energy for concentric $\delta$-${\delta }^{\prime }$ spheres
• Repulsive Casimir-Lifshitz pressure in closed cavities

Cited by in corpus (3)

• Casimir energy for spinor fields with $\delta$-shell potentials
• Generalized Neumann boundary condition for the scalar field
• Vacuum energy of scalar fields on spherical shells with general matching conditions