# Zeta-function approach to Casimir energy with singular potentials

## Abstract

In the framework of zeta-function approach the Casimir energy for three simple model system: single delta potential, step function potential and three delta potentials are analyzed. It is shown that the energy contains contributions which are peculiar to the potentials. It is suggested to renormalize the energy using the condition that the energy of infinitely separated potentials is zero which corresponds to subtraction all terms of asymptotic expansion of zeta-function. The energy obtained in this way obeys all physically reasonable conditions. It is finite in the Dirichlet limit, and it may be attractive or repulsive depending on the strength of potential. The effective action is calculated, and it is shown that the surface contribution appears. The renormalization of the effective action is discussed.

- Authors:

- Departamento de Fisica, Universidade Federal da Paraiba, Caixa Postal 5008, CEP 58051-970 Joao Pessoa, Pb (Brazil)

- Publication Date:

- OSTI Identifier:
- 20795747

- Resource Type:
- Journal Article

- Resource Relation:
- Journal Name: Physical Review. D, Particles Fields; Journal Volume: 73; Journal Issue: 2; Other Information: DOI: 10.1103/PhysRevD.73.025003; (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; ACTION INTEGRAL; CASIMIR EFFECT; EXPANSION; PHI4-FIELD THEORY; POTENTIALS; RENORMALIZATION

### Citation Formats

```
Khusnutdinov, Nail R.
```*Zeta-function approach to Casimir energy with singular potentials*. United States: N. p., 2006.
Web. doi:10.1103/PHYSREVD.73.0.

```
Khusnutdinov, Nail R.
```*Zeta-function approach to Casimir energy with singular potentials*. United States. doi:10.1103/PHYSREVD.73.0.

```
Khusnutdinov, Nail R. Sun .
"Zeta-function approach to Casimir energy with singular potentials". United States.
doi:10.1103/PHYSREVD.73.0.
```

```
@article{osti_20795747,
```

title = {Zeta-function approach to Casimir energy with singular potentials},

author = {Khusnutdinov, Nail R.},

abstractNote = {In the framework of zeta-function approach the Casimir energy for three simple model system: single delta potential, step function potential and three delta potentials are analyzed. It is shown that the energy contains contributions which are peculiar to the potentials. It is suggested to renormalize the energy using the condition that the energy of infinitely separated potentials is zero which corresponds to subtraction all terms of asymptotic expansion of zeta-function. The energy obtained in this way obeys all physically reasonable conditions. It is finite in the Dirichlet limit, and it may be attractive or repulsive depending on the strength of potential. The effective action is calculated, and it is shown that the surface contribution appears. The renormalization of the effective action is discussed.},

doi = {10.1103/PHYSREVD.73.0},

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

number = 2,

volume = 73,

place = {United States},

year = {Sun Jan 15 00:00:00 EST 2006},

month = {Sun Jan 15 00:00:00 EST 2006}

}