Vacuum energy of a massive scalar field in the presence of a semi-transparent cylinder

Abstract

We compute the ground state energy of a massive scalar field in the background of a cylindrical shell whose potential is given by a delta function. The zero point energy is expressed in terms of the Jost function of the related scattering problem, the renormalization is performed with the help of the heat kernel expansion. The energy is found to be negative for attractive and for repulsive backgrounds as well.

17 pages, 5 figures

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• How does Casimir energy fall? IV. Gravitational interaction of regularized quantum vacuum energy
• Massive 3+1 Aharonov-Bohm fermions in an MIT cylinder
• Vacuum energy in conical space with additional boundary conditions
• Local and Global Casimir Energies: Divergences, Renormalization, and the Coupling to Gravity
• Zeta-function approach to Casimir energy with singular potentials
• Parity violating cylindrical shell in the framework of QED
• Recent Developments in Quantum Vacuum Energy for Confined Fields
• Vacuum polarization by a magnetic flux of special rectangular form