# Supercharge Operator of Hidden Symmetry in the Dirac Equation

## Abstract

We require that there exist some additional symmetry of the Dirac Hamiltonian in an arbitrary central potential which describes the degeneracy of spectrum with respect to the two signs of eigenvalues of famous Dirac's K operator. It is proved that this happens only for the Coulomb potential. In this particular case symmetry operator reduces to the well-known Johnson-Lippmann operator, which plays a role of supercharge in the Dirac-Coulomb problem and generates a Witten's superalgebra.

- Authors:

- Department of Theoretical Physics, Ivane Javakhishvili Tbilisi State University, I.Chavchavadze ave. 3, 0128, Tbilisi (Georgia)

- Publication Date:

- OSTI Identifier:
- 20900819

- Resource Type:
- Journal Article

- Resource Relation:
- Journal Name: AIP Conference Proceedings; Journal Volume: 881; Journal Issue: 1; Conference: CICHEP II: Cairo international conference on high energy physics, Cairo (Egypt), 14-17 Jan 2006; Other Information: DOI: 10.1063/1.2435304; (c) 2007 American Institute of Physics; Country of input: International Atomic Energy Agency (IAEA)

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; CENTRAL POTENTIAL; COULOMB FIELD; DIRAC EQUATION; EIGENVALUES; HAMILTONIANS; SUPERSYMMETRY

### Citation Formats

```
Khachidze, Tamari T., and Khelashvili, Anzor A.
```*Supercharge Operator of Hidden Symmetry in the Dirac Equation*. United States: N. p., 2007.
Web. doi:10.1063/1.2435304.

```
Khachidze, Tamari T., & Khelashvili, Anzor A.
```*Supercharge Operator of Hidden Symmetry in the Dirac Equation*. United States. doi:10.1063/1.2435304.

```
Khachidze, Tamari T., and Khelashvili, Anzor A. Fri .
"Supercharge Operator of Hidden Symmetry in the Dirac Equation". United States.
doi:10.1063/1.2435304.
```

```
@article{osti_20900819,
```

title = {Supercharge Operator of Hidden Symmetry in the Dirac Equation},

author = {Khachidze, Tamari T. and Khelashvili, Anzor A.},

abstractNote = {We require that there exist some additional symmetry of the Dirac Hamiltonian in an arbitrary central potential which describes the degeneracy of spectrum with respect to the two signs of eigenvalues of famous Dirac's K operator. It is proved that this happens only for the Coulomb potential. In this particular case symmetry operator reduces to the well-known Johnson-Lippmann operator, which plays a role of supercharge in the Dirac-Coulomb problem and generates a Witten's superalgebra.},

doi = {10.1063/1.2435304},

journal = {AIP Conference Proceedings},

number = 1,

volume = 881,

place = {United States},

year = {Fri Jan 12 00:00:00 EST 2007},

month = {Fri Jan 12 00:00:00 EST 2007}

}

DOI: 10.1063/1.2435304

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