# Casimir force between planes as a boundary finite size effect

## Abstract

The ground state energy of a boundary quantum field theory is derived in planar geometry in D+1-dimensional spacetime. It provides a universal expression for the Casimir energy which exhibits its dependence on the boundary conditions via the reflection amplitudes of the low energy particle excitations. We demonstrate the easy and straightforward applicability of the general expression by analyzing the free scalar field with Robin boundary condition and by rederiving the most important results available in the literature for this geometry.

- Authors:

- Theoretical Physics Research Group, Hungarian Academy of Sciences, 1117 Budapest, Pazmany Peter setany 1/A (Hungary)
- Institute for Theoretical Physics, Eoetvoes University, 1117 Budapest, Pazmany Peter setany 1/A (Hungary)

- Publication Date:

- OSTI Identifier:
- 20782672

- Resource Type:
- Journal Article

- Resource Relation:
- Journal Name: Physical Review. D, Particles Fields; Journal Volume: 73; Journal Issue: 6; Other Information: DOI: 10.1103/PhysRevD.73.065001; (c) 2006 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; AMPLITUDES; BOUNDARY CONDITIONS; CASIMIR EFFECT; EXCITATION; GEOMETRY; GROUND STATES; ONE-DIMENSIONAL CALCULATIONS; QUANTUM FIELD THEORY; REFLECTION; SCALAR FIELDS; SPACE-TIME

### Citation Formats

```
Bajnok, Z., Takacs, G., and Palla, L.
```*Casimir force between planes as a boundary finite size effect*. United States: N. p., 2006.
Web. doi:10.1103/PHYSREVD.73.065001.

```
Bajnok, Z., Takacs, G., & Palla, L.
```*Casimir force between planes as a boundary finite size effect*. United States. doi:10.1103/PHYSREVD.73.065001.

```
Bajnok, Z., Takacs, G., and Palla, L. Wed .
"Casimir force between planes as a boundary finite size effect". United States.
doi:10.1103/PHYSREVD.73.065001.
```

```
@article{osti_20782672,
```

title = {Casimir force between planes as a boundary finite size effect},

author = {Bajnok, Z. and Takacs, G. and Palla, L.},

abstractNote = {The ground state energy of a boundary quantum field theory is derived in planar geometry in D+1-dimensional spacetime. It provides a universal expression for the Casimir energy which exhibits its dependence on the boundary conditions via the reflection amplitudes of the low energy particle excitations. We demonstrate the easy and straightforward applicability of the general expression by analyzing the free scalar field with Robin boundary condition and by rederiving the most important results available in the literature for this geometry.},

doi = {10.1103/PHYSREVD.73.065001},

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

number = 6,

volume = 73,

place = {United States},

year = {Wed Mar 15 00:00:00 EST 2006},

month = {Wed Mar 15 00:00:00 EST 2006}

}

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