Casimir piston for massless scalar fields in three dimensions

Abstract

We study the Casimir piston for massless scalar fields obeying Dirichlet boundary conditions in a three dimensional cavity with sides of arbitrary lengths $a,b$ and $c$ where $a$ is the plate separation. We obtain an exact expression for the Casimir force on the piston valid for any values of the three lengths. As in the electromagnetic case with perfect conductor conditions, we find that the Casimir force is negative (attractive) regardless of the values of $a$, $b$ and $c$. Though cases exist where the interior contributes a positive (repulsive) Casimir force, the total Casimir force on the piston is negative when the exterior contribution is included. We also obtain an alternative expression for the Casimir force that is useful computationally when the plate separation $a$ is large.

19 pages,3 figures; references updated and typos fixed to match published version

References in corpus (17)

• New Developments in the Casimir Effect
• Opposites Attract - A Theorem About The Casimir Force
• The Dirichlet Casimir Problem
• Casimir effect in de Sitter and Anti-de Sitter braneworlds
• Attractive Casimir Forces in a Closed Geometry
• Casimir force on a piston
• Analog gravity from field theory normal modes?
• Systematics of the Relationship between Vacuum Energy Calculations and Heat Kernel Coefficients
• Multidimensional extension of the generalized Chowla-Selberg formula
• Multidimensional cut-off technique, odd-dimensional Epstein zeta functions and Casimir energy of massless scalar fields
• Casimir-like force arising from quantum fluctuations in a slow-moving dilute Bose-Einstein condensate
• Explicit Zeta Functions for Bosonic and Fermionic Fields on a Noncommutative Toroidal Spacetime
• Casimir forces in Bose-Einstein condensates: finite size effects in three-dimensional rectangular cavities
• Spectral asymptotics of Euclidean quantum gravity with diff-invariant boundary conditions
• Zeta function regularization for a scalar field in a compact domain
• One-loop effective potential from higher-dimensional AdS black holes
• Heat kernel coefficients for chiral bag boundary conditions

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