# On Dirac-Coulomb problem in (2+1) dimensional space-time and path integral quantization

## Abstract

The problem of Dirac particle interacting with Coulomb potential in (2+1) dimensions is formulated in the framework of super-symmetric path integrals where the spin degrees of freedom are described by odd Grassmannian variables. The relative propagator is expressed through Cartesian coordinates in a Hamiltonian form by the use of an adequate transformation. The passage to the polar coordinates permitted us to calculate the fixed energy Green's function and to extract bound states and associating wave functions.

- Authors:

- L.P.Th, Departement de physique, Universite de Jijel, BP 98, Ouled Aissa, Jijel 18000 (Algeria)
- Departement de Physique, Faculte de Sciences, Universite Mentouri, Route Ain El-Bey, Constantine 25000 (Algeria)

- Publication Date:

- OSTI Identifier:
- 22093614

- Resource Type:
- Journal Article

- Journal Name:
- Journal of Mathematical Physics

- Additional Journal Information:
- Journal Volume: 53; Journal Issue: 6; Other Information: (c) 2012 American Institute of Physics; Country of input: International Atomic Energy Agency (IAEA); Journal ID: ISSN 0022-2488

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; BOUND STATE; CARTESIAN COORDINATES; CONFIGURATION; COULOMB FIELD; DEGREES OF FREEDOM; DIRAC EQUATION; GREEN FUNCTION; HAMILTONIANS; PATH INTEGRALS; QUANTIZATION; SPACE-TIME; SPIN; SUPERSYMMETRY; THREE-DIMENSIONAL CALCULATIONS; TRANSFORMATIONS; WAVE FUNCTIONS

### Citation Formats

```
Haouat, S., and Chetouani, L.
```*On Dirac-Coulomb problem in (2+1) dimensional space-time and path integral quantization*. United States: N. p., 2012.
Web. doi:10.1063/1.4725418.

```
Haouat, S., & Chetouani, L.
```*On Dirac-Coulomb problem in (2+1) dimensional space-time and path integral quantization*. United States. doi:10.1063/1.4725418.

```
Haouat, S., and Chetouani, L. Fri .
"On Dirac-Coulomb problem in (2+1) dimensional space-time and path integral quantization". United States. doi:10.1063/1.4725418.
```

```
@article{osti_22093614,
```

title = {On Dirac-Coulomb problem in (2+1) dimensional space-time and path integral quantization},

author = {Haouat, S. and Chetouani, L.},

abstractNote = {The problem of Dirac particle interacting with Coulomb potential in (2+1) dimensions is formulated in the framework of super-symmetric path integrals where the spin degrees of freedom are described by odd Grassmannian variables. The relative propagator is expressed through Cartesian coordinates in a Hamiltonian form by the use of an adequate transformation. The passage to the polar coordinates permitted us to calculate the fixed energy Green's function and to extract bound states and associating wave functions.},

doi = {10.1063/1.4725418},

journal = {Journal of Mathematical Physics},

issn = {0022-2488},

number = 6,

volume = 53,

place = {United States},

year = {2012},

month = {6}

}

DOI: 10.1063/1.4725418

Other availability

Save to My Library

You must Sign In or Create an Account in order to save documents to your library.