Spectral Zeta Functions for a Cylinder and a Circle

Abstract

Spectral zeta functions $\zeta (s)$ for the massless scalar fields obeying the Dirichlet and Neumann boundary conditions on a surface of an infinite cylinder are constructed. These functions are defined explicitly in a finite domain of the complex plane s containing the closed interval of real axis $-1\le$ Re $s\le 0$. Proceeding from this the spectral zeta functions for the boundary conditions given on a circle (boundary value problem on a plane) are obtained without any additional calculations. The Casimir energy for the relevant field configurations is deduced.

REVTeX4, 13 pages, no tables and figures; v2 some misprints are corrected

References in corpus (1)

• Zeta Functions and the Casimir Energy

Cited by in corpus (23)

• New Developments in the Casimir Effect
• Heat kernel expansion: user's manual
• Calculating Casimir Energies in Renormalizable Quantum Field Theory
• Local and Global Casimir Energies for a Semitransparent Cylindrical Shell
• Casimir Energy of a Semi-Circular Infinite Cylinder
• Radiative Correction to the Dirichlet Casimir Energy for $\lambda {\varphi }^4$ Theory in Two Spatial Dimensions
• Vacuum energy in conical space with additional boundary conditions
• Local and Global Casimir Energies: Divergences, Renormalization, and the Coupling to Gravity
• Casimir Energy for a Coupled Fermion-Kink System and its stability
• Weyl problem and Casimir effects in spherical shell geometry
• Casimir effect due to a single boundary as a manifestation of the Weyl problem
• Zero-point energy in spheroidal geometries
• Semiclassical Estimates of Electromagnetic Casimir Self-Energies of Spherical and Cylindrical Metallic Shells
• Surface modes and photonic modes in Casimir calculations for a compact cylinder
• A perturbative approach to the spectral zeta functions of strings, drums and quantum billiards
• Casimir energy calculation for massive scalar field on spherical surfaces: an alternative approach
• Casimir energy of a cylindrical shell of elliptical cross section
• Radiative Correction to the Casimir Energy for Lorentz-violating Scalar Field in d+1 Dimensions
• Recent Developments in Quantum Vacuum Energy for Confined Fields
• Casimir energy of smooth compact surfaces
• Aharonov-Bohm magnetism and Landau diamagnetism in semimetals
• One-Loop Correction to the Casimir Energy in Lorentz-Violating ${\varphi }^4$ Theory with Rough Membrane Boundaries
• Vacuum Polarization and Casimir Energy of a Dirac Field Induced by a Scalar Potential in One Spatial Dimension