Scalar Casimir densities for cylindrically symmetric Robin boundaries

Abstract

Wightman function, the vacuum expectation values of the field square and the energy-momentum tensor are investigated for a massive scalar field with general curvature coupling parameter in the region between two coaxial cylindrical boundaries. It is assumed that the field obeys general Robin boundary conditions on bounding surfaces. The application of a variant of the generalized Abel-Plana formula allows to extract from the expectation values the contribution from single shells and to present the interference part in terms of exponentially convergent integrals. The vacuum forces acting on the boundaries are presented as the sum of self-action and interaction terms. The first one contains well-known surface divergences and needs a further renormalization. The interaction forces between the cylindrical boundaries are finite and are attractive for special cases of Dirichlet and Neumann scalars. For the general Robin case the interaction forces can be both attractive or repulsive depending on the coefficients in the boundary conditions. The total Casimir energy is evaluated by using the zeta function regularization technique. It is shown that it contains a part which is located on bounding surfaces. The formula for the interference part of the surface energy is derived and the energy balance is discussed.

arXiv comment22 pages, 5 figures

References in corpus (42)

• New Developments in the Casimir Effect
• Bulk Fields and Supersymmetry in a Slice of AdS
• Calculating Vacuum Energies in Renormalizable Quantum Field Theories: A New Approach to the Casimir Problem
• Casimir Effect on the Worldline
• Path Integral Approach to the Dynamic Casimir Effect with Fluctuating Boundaries
• Casimir effect for curved geometries: PFA validity limits
• Casimir effect for scalar fields under Robin boundary conditions on plates
• The Dirichlet Casimir Problem
• The Casimir Effect and Geometric Optics
• Casimir Energies in Light of Quantum Field Theory
• The generalized Abel-Plana formula with applications to Bessel functions and Casimir effect
• Casimir Effects: An Optical Approach I. Foundations and Examples
• Mode-by-mode summation for the zero point electromagnetic energy of an infinite cylinder
• Quantized bulk scalar fields in the Randall-Sundrum brane-model
• Systematics of the Relationship between Vacuum Energy Calculations and Heat Kernel Coefficients
• Energy of the vacuum with a perfectly conducting and infinite cylindrical surface
• Casimir interaction between two concentric cylinders: exact versus semiclassical results
• Surface Casimir densities and induced cosmological constant on parallel branes in AdS
• Wightman function and Casimir densities on AdS bulk with application to the Randall-Sundrum braneworld
• Vacuum Energy Density near Fluctuating Boundaries
• Vacuum energy in a spherically symmetric background field
• Scalar Casimir effect for D-dimensional spherically symmetric Robin boundaries
• On the energy-momentum tensor for a scalar field on manifolds with boundaries
• Towards a Theory of Molecular Forces between Deformed Media
• Casimir Effects in Renormalizable Quantum Field Theories
• Casimir Energy for a Purely Dielectric Cylinder by the Mode Summation Method
• Casimir Energy for a Dielectric Cylinder
• The ground state energy of a spinor field in the background of a finite radius flux tube
• Regularized Casimir energy for an infinite dielectric cylinder subject to light-velocity conservation
• Vacuum densities and zero-point energy for fields obeying Robin conditions on cylindrical surfaces
• Casimir Energy of a Ball and Cylinder in the Zeta Function Technique
• Casimir energy of a compact cylinder under the condition $\epsilon \mu =c^{-2}$
• Casimir force between eccentric cylinders
• Synchrotron radiation from a charge moving along a helical orbit inside a dielectric cylinder
• Casimir Energy of a Semi-Circular Infinite Cylinder
• Local Casimir Energy for a Wedge with circular outer boundary
• Casimir energy and realistic model of dilute dielectric ball
• Mixed Boundary Conditions in Euclidean Quantum Gravity
• Boundary conditions and the entropy bound
• Vacuum Energy and Casimir Force in a Presence of Skin-depth Dependent Boundary Condition
• Radiation from an oscillator uniformly moving along the axis of a dielectric cylinder
• Whightman function and scalar Casimir densities for a wedge with a cylindrical boundary

Cited by in corpus (8)

• The generalized Abel-Plana formula with applications to Bessel functions and Casimir effect
• Electromagnetic Casimir densities for a wedge with a coaxial cylindrical shell
• Semiclassical Estimates of Electromagnetic Casimir Self-Energies of Spherical and Cylindrical Metallic Shells
• Wightman function and scalar Casimir densities for a wedge with two cylindrical boundaries
• A summation formula over the zeros of a combination of the associated Legendre functions with a physical application
• Summation formula over the zeros of the associated Legendre function with a physical application
• Scalar Casimir densities induced by a cylindrical shell in de Sitter spacetime
• Casimir interaction between two concentric cylinders at nonzero temperature