Casimir effect for a perfectly conducting wedge in terms of local zeta function

Abstract

The vacuum energy density of electromagnetic field inside a perfectly conducting wedge is calculated by making use of the local zeta function technique. This regularization completely eliminates divergent expressions in the course of calculations and gives rise to a finite expression for the energy density in question without any subtractions. Employment of the Hertz potentials for constructing the general solution to the Maxwell equations results in a considerable simplification of the calculations. Transition to the global zeta function is carried out by introducing a cutoff nearby the cusp at the origin. Proceeding from this the heat kernel coefficients are calculated and the high temperature asymptotics of the Helmholtz free energy and of the torque of the Casimir forces are found. The wedge singularity gives rise to a specific high temperature behaviour $\sim T^2$ of the quantities under consideration. The obtained results are directly applicable to the free energy of a scalar massless field and electromagnetic field on the background of a cosmic string.

20 pages, REVTeX, no figures, no tables

References in corpus (3)

• New Developments in the Casimir Effect
• High temperature asymptotics of thermodynamic functions of electromagnetic field subjected to boundary conditions on a sphere and cylinder
• Casimir Effect for a Dielectric Wedge

Cited by in corpus (16)

• 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
• Electromagnetic Casimir densities for a wedge with a coaxial cylindrical shell
• The Electromagnetic Field Stress Tensor between Dielectric Half-Spaces
• 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
• Wightman function and scalar Casimir densities for a wedge with two cylindrical boundaries
• Scalar Casimir densities and forces for parallel plates in cosmic string spacetime
• Electromagnetic Casimir Effect in Wedge Geometry and the Energy-Momentum Tensor in Media
• Local zeta regularization and the scalar Casimir effect II. Some explicitly solvable cases