Vacuum energy in a spherically symmetric background field

Abstract

The vacuum energy of a scalar field in a spherically symmetric background field is considered. It is expressed through the Jost function of the corresponding scattering problem. The renormalization is discussed in detail and performed using the uniform asymptotic expansion of the Jost function. The method is demonstrated in a simple explicit example.

14 pages, 1 Postscript figure

References in corpus (5)

• Zeta Functions and the Casimir Energy
• Heat-kernel coefficients of the Laplace operator on the D-dimensional ball
• One-Loop Corrections to Bubble Nucleation Rate at Finite Temperature
• The Exact Critical Bubble Free Energy and the Effectiveness of Effective Potential Approximations
• Evaluation of the One-loop Effective Action at Zero and Finite Temperature

Cited by in corpus (56)

• New Developments in the Casimir Effect
• Calculating Vacuum Energies in Renormalizable Quantum Field Theories: A New Approach to the Casimir Problem
• Casimir energies for massive fields in the bag
• On the ground state energy for a penetrable sphere and for a dielectric ball
• The generalized Abel-Plana formula with applications to Bessel functions and Casimir effect
• Casimir Effect: The Classical Limit
• Ground State Energy of Massive Scalar Field in the Background of Finite Thickness Cosmic String
• Functional determinants for radial operators
• Nonsmooth backgrounds in quantum field theory
• Casimir's energy of a conducting sphere and of a dilute dielectric ball
• The ground state energy of a spinor field in the background of a finite radius flux tube
• Casimir energy-momentum tensor for a brane in de Sitter spacetime
• Path integral quantization of electrodynamics in dielectric media
• Heat kernel Coefficients and Divergencies of the Casimir Energy for the Dispersive Sphere
• The heat kernel coefficients for the dielectric cylinder
• Multiple reflection expansion and heat kernel coefficients
• Ground state energy in a wormhole space-time
• Casimir effect in a wormhole spacetime
• The ground state energy of a massive scalar field in the background of a semi-transparent spherical shell
• Fermionic Vacuum Energy from a Nielsen-Olesen Vortex
• Massive field contributions to the QCD vacuum tunneling amplitude
• Neutrino ground state in a dense star
• Semiclassical wormholes
• Ground State Energy of Massive Scalar Field Inside a Spherical Region in the Global Monopole Background
• Quantum Corrections to Soliton Energies
• On the Vacuum energy of a Color Magnetic Vortex
• Electromagnetic Casimir densities for a wedge with a coaxial cylindrical shell
• Vacuum energy of a massive scalar field in the presence of a semi-transparent cylinder
• Massive 3+1 Aharonov-Bohm fermions in an MIT cylinder
• Vacuum energy in the presence of a magnetic string with delta function profile
• Dependence of the vacuum energy on spherically symmetric background fields
• Casimir energies in spherically symmetric background potentials revisited
• Casimir Energy for concentric $\delta$-${\delta }^{\prime }$ spheres
• Scalar Casimir densities for cylindrically symmetric Robin boundaries
• Casimir Effect in the Presence of External Fields
• On the entropy of a spherical plasma shell
• Dressing Up the Kink
• Spectral Methods for Coupled Channels with a Mass Gap
• Wightman function and scalar Casimir densities for a wedge with two cylindrical boundaries
• Report of the Detailed Calculation of the Effective Potential in Spacetimes with $S^1\times R^d$ Topology and at Finite Temperature
• Summation formula over the zeros of the associated Legendre function with a physical application
• A summation formula over the zeros of a combination of the associated Legendre functions with a physical application
• Casimir self-energy of a δ-δ' sphere
• Vacuum polarization energy of a complex scalar field in a vortex background
• Quantum energies of BPS vortices in $D=2+1$ and $D=3+1$
• Photon Green's function and the Casimir energy in a medium
• Dependence of scalar matter vacuum energy, induced by a magnetic topological defect, on the coupling to space-time curvature
• Casimir energy for spinor fields with $\delta$-shell potentials
• Functional determinants and Casimir energy in higher dimensional spherically symmetric background potentials
• Simplified Vacuum Energy Expressions for Radial Backgrounds and Domain Walls
• Vacuum Energy of Quantum Fields in Classical Background Configurations
• Vacuum polarization by a magnetic flux of special rectangular form
• Quantum effects on winding configurations in SU(2)-Higgs theory
• Vacuum energy of scalar fields on spherical shells with general matching conditions
• Spherical Casimir effect for a massive scalar field on the three dimensional ball
• Vacuum energy for a scalar field with self-interaction in (1+1) dimensions