# 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.

- Authors:

- Physics Department, Bishop's University, 2600 College Street, Sherbrooke, Quebec, J1M0C8 (Canada)

- Publication Date:

- OSTI Identifier:
- 20935271

- Resource Type:
- Journal Article

- Resource Relation:
- Journal Name: Physical Review. D, Particles Fields; Journal Volume: 75; Journal Issue: 10; Other Information: DOI: 10.1103/PhysRevD.75.105012; (c) 2007 The American Physical Society; Country of input: International Atomic Energy Agency (IAEA)

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; BOUNDARY CONDITIONS; CASIMIR EFFECT; PISTONS; SCALAR FIELDS; THREE-DIMENSIONAL CALCULATIONS

### Citation Formats

```
Edery, Ariel.
```*Casimir piston for massless scalar fields in three dimensions*. United States: N. p., 2007.
Web. doi:10.1103/PHYSREVD.75.105012.

```
Edery, Ariel.
```*Casimir piston for massless scalar fields in three dimensions*. United States. doi:10.1103/PHYSREVD.75.105012.

```
Edery, Ariel. Tue .
"Casimir piston for massless scalar fields in three dimensions". United States.
doi:10.1103/PHYSREVD.75.105012.
```

```
@article{osti_20935271,
```

title = {Casimir piston for massless scalar fields in three dimensions},

author = {Edery, Ariel},

abstractNote = {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.},

doi = {10.1103/PHYSREVD.75.105012},

journal = {Physical Review. D, Particles Fields},

number = 10,

volume = 75,

place = {United States},

year = {Tue May 15 00:00:00 EDT 2007},

month = {Tue May 15 00:00:00 EDT 2007}

}