Comment on the sign of the Casimir force

Abstract

I show that reflection positivity implies that the force between any mirror pair of charge-conjugate probes of the quantum vacuum is attractive. This generalizes a recent theorem of Kenneth and Klich to interacting quantum fields, to arbitrary semiclassical bodies, and to quantized probes with non-overlapping wavefunctions. I also prove that the torques on charge-conjugate probes tend always to rotate them into a mirror-symmetric position.

13 pages, 1 figure, Latex file. Several points clarified and expanded, two references added.

References in corpus (13)

• New Developments in the Casimir Effect
• Nonlinear Micromechanical Casimir Oscillator
• Sub-millimeter Tests of the Gravitational Inverse-square Law
• Stiction, Adhesion Energy and the Casimir Effect in Micromechanical Systems
• Opposites Attract - A Theorem About The Casimir Force
• Constraining New Forces in the Casimir Regime Using the Isoelectronic Technique
• Metastability and the Casimir Effect in Micromechanical Systems
• The Dirichlet Casimir Problem
• Constraints on Yukawa-Type Deviations from Newtonian Gravity at 20 Microns
• Casimir force on a piston
• Movement and Fluctuations of the Vacuum
• Casimir interaction between normal or superfluid grains in the Fermi sea
• A critical comparison of different definitions of topological charge on the lattice

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• Casimir forces in a T operator approach
• Tunable Casimir repulsion with three dimensional topological insulators
• Repulsive Casimir effect from extra dimensions and Robin boundary conditions: from branes to pistons
• Constraints on stable equilibria with fluctuation-induced forces
• Repulsive Casimir Effect with Chern insulators
• Crossover from Attractive to Repulsive Casimir Forces and Vice Versa
• Aspect-ratio dependence of thermodynamic Casimir forces
• Sign Flip in the Casimir Force for Interacting Fermion Systems
• Phases of Holographic Interfaces
• Large-$n$ approach to thermodynamic Casimir effects in slabs with free surfaces
• The Casimir effect in topological matter
• Tunable critical Casimir forces counteract Casimir-Lifshitz attraction
• The Casimir effect as a sum-over-modes in dissipative systems
• Fluctuation-induced forces in strongly anisotropic critical systems
• Cancellation of nonrenormalizable hypersurface divergences and the d-dimensional Casimir piston
• Vacuum Stress and Closed Paths in Rectangles, Pistons, and Pistols
• Finite temperature Casimir effect in piston geometry and its classical limit
• Casimir force in O(n) lattice models with a diffuse interface
• Critical Casimir effect in films for generic non-symmetry-breaking boundary conditions
• Casimir Piston of Real Materials and its Application to Multi-Layer Models
• Finite temperature Casimir effect of massive fermionic fields in the presence of compact dimensions
• Casimir Force for the $\mathbb{C}{P}^{N-1}$ Model
• Van der Waals torque and force between anisotropic topological insulator slabs
• Casimir Energy for concentric $\delta$-${\delta }^{\prime }$ spheres
• Bulk and boundary effects on the decay of the thermodynamic Casimir force
• Critical Casimir interaction between colloidal Janus-type particles in two spatial dimensions
• Geometry and material effects in Casimir physics - Scattering theory
• Numerical Analysis of some Generalized Casimir Pistons
• Classification of the sign of the critical Casimir force in two dimensional systems at asymptotically large separations
• Gravitating Opposites Attract
• Conformal field theory of critical Casimir forces between surfaces with alternating boundary conditions in two dimensions
• Repulsive Casimir-Lifshitz pressure in closed cavities
• Holographic dual of defect CFT with corner contributions
• Irreducible Scalar Many-Body Casimir Energies: Theorems and Numerical Studies
• Bound of Casimir Effect by Holography
• General Junction Condition and Casimir Effect for (1+1)-Dimensional Scalar Network CFT
• Reversing the Critical Casimir force by shape deformation
• Casimir-Lifshitz pressure on cavity walls