Three-dimensional Casimir piston for massive scalar fields

Journal Article · Sat Aug 15 04:00:00 EDT 2009 · Annals of Physics (New York)

DOI:https://doi.org/10.1016/j.aop.2009.05.006· OSTI ID:21313060

We consider Casimir force acting on a three-dimensional rectangular piston due to a massive scalar field subject to periodic, Dirichlet and Neumann boundary conditions. Exponential cut-off method is used to derive the Casimir energy. It is shown that the divergent terms do not contribute to the Casimir force acting on the piston, thus render a finite well-defined Casimir force acting on the piston. Explicit expressions for the total Casimir force acting on the piston is derived, which show that the Casimir force is always attractive for all the different boundary conditions considered. As a function of a - the distance from the piston to the opposite wall, it is found that the magnitude of the Casimir force behaves like 1/a{sup 4} when a{yields}0{sup +} and decays exponentially when a{yields}{infinity}. Moreover, the magnitude of the Casimir force is always a decreasing function of a. On the other hand, passing from massless to massive, we find that the effect of the mass is insignificant when a is small, but the magnitude of the force is decreased for large a in the massive case.

• OSTI ID: 21313060
• Journal Information: Annals of Physics (New York), Journal Name: Annals of Physics (New York) Journal Issue: 8 Vol. 324; ISSN 0003-4916; ISSN APNYA6
• Country of Publication: United States
• Language: English

Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
BOUNDARY CONDITIONS
CASIMIR EFFECT
DIRICHLET PROBLEM
FUNCTIONS
PERIODICITY
PISTONS
SCALAR FIELDS
THREE-DIMENSIONAL CALCULATIONS