Casimir Energy of a Semi-Circular Infinite Cylinder

Abstract

The Casimir energy of a semi-circular cylindrical shell is calculated by making use of the zeta function technique. This shell is obtained by crossing an infinite circular cylindrical shell by a plane passing through the symmetry axes of the cylinder and by considering only a half of this configuration. All the surfaces, including the cutting plane, are assumed to be perfectly conducting. The zeta functions for scalar massless fields obeying the Dirichlet and Neumann boundary conditions on the semi-circular cylinder are constructed exactly. The sum of these zeta functions gives the zeta function for electromagnetic field in question. The relevant plane problem is considered also. In all the cases the final expressions for the corresponding Casimir energies contain the pole contributions which are the consequence of the edges or corners in the boundaries. This implies that further renormalization is needed in order for the finite physical values for vacuum energy to be obtained for given boundary conditions.

REVTeX, 16 pages, 1 figure in a separate fig1.eps file; revised version accepted for publication in J. Math. Phys

References in corpus (5)

• Heat kernel asymptotics with mixed boundary conditions
• Casimir Energies for Spherically Symmetric Cavities
• Casimir energy of a compact cylinder under the condition $\epsilon \mu =c^{-2}$
• Spectral Zeta Functions for a Cylinder and a Circle
• Divergences in the Casimir energy

Cited by in corpus (22)

• Heat kernel expansion: user's manual
• Nonsmoothness of the boundary and the relevant heat kernel coefficients
• Casimir effect in quadratic theories of gravity
• Casimir effect in Post-Newtonian Gravity with Lorentz-violation
• Casimir Effect for a Semitransparent Wedge and an Annular Piston
• Casimir effect in Extended Theories of Gravity
• Repulsive Casimir-Polder forces from cosmic strings
• Local Casimir Energy for a Wedge with circular outer boundary
• Electromagnetic Casimir densities for a wedge with a coaxial cylindrical shell
• Electrodynamic Casimir Effect in a Medium-Filled Wedge II
• Electrodynamic Casimir Effect in a Medium-Filled Wedge
• Vacuum energy in conical space with additional boundary conditions
• Casimir effect at nonzero temperature for wedges and cylinders
• Heuristic derivation of the Casimir effect from Generalized Uncertainty Principle
• Weyl problem and Casimir effects in spherical shell geometry
• Whightman function and scalar Casimir densities for a wedge with a cylindrical boundary
• Scalar Casimir densities for cylindrically symmetric Robin boundaries
• Casimir effect due to a single boundary as a manifestation of the Weyl problem
• Wightman function and scalar Casimir densities for a wedge with two cylindrical boundaries
• Scalar Casimir densities induced by a cylindrical shell in de Sitter spacetime
• Divergences in the Casimir energy
• Electromagnetic Casimir Effect in Wedge Geometry and the Energy-Momentum Tensor in Media