### Abstract

We obtain and analyze equations determining first-order differential symmetry operators with matrix coefficients for the Dirac equation with an external electromagnetic potential in a (2 + 1)-dimensional Riemann (curved) spacetime. Nonequivalent complete sets of mutually commuting symmetry operators are classified in a (2 + 1)-dimensional Minkowski (flat) space. For each of the sets, we carry out a complete separation of variables in the Dirac equation and find a corresponding electromagnetic potential permitting separation of variables.

Original language | English |
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Article number | 1850085 |

Journal | International Journal of Geometric Methods in Modern Physics |

Volume | 15 |

Issue number | 5 |

DOIs | |

Publication status | Published - 1 May 2018 |

### Fingerprint

### Keywords

- (2 + 1)-dimensional Dirac equation
- separation of variables
- symmetry operators

### ASJC Scopus subject areas

- Physics and Astronomy (miscellaneous)

### Cite this

**Symmetry operators and separation of variables in the (2 + 1)-dimensional Dirac equation with external electromagnetic field.** / Shapovalov, A. V.; Breev, A. I.

Research output: Contribution to journal › Article

}

TY - JOUR

T1 - Symmetry operators and separation of variables in the (2 + 1)-dimensional Dirac equation with external electromagnetic field

AU - Shapovalov, A. V.

AU - Breev, A. I.

PY - 2018/5/1

Y1 - 2018/5/1

N2 - We obtain and analyze equations determining first-order differential symmetry operators with matrix coefficients for the Dirac equation with an external electromagnetic potential in a (2 + 1)-dimensional Riemann (curved) spacetime. Nonequivalent complete sets of mutually commuting symmetry operators are classified in a (2 + 1)-dimensional Minkowski (flat) space. For each of the sets, we carry out a complete separation of variables in the Dirac equation and find a corresponding electromagnetic potential permitting separation of variables.

AB - We obtain and analyze equations determining first-order differential symmetry operators with matrix coefficients for the Dirac equation with an external electromagnetic potential in a (2 + 1)-dimensional Riemann (curved) spacetime. Nonequivalent complete sets of mutually commuting symmetry operators are classified in a (2 + 1)-dimensional Minkowski (flat) space. For each of the sets, we carry out a complete separation of variables in the Dirac equation and find a corresponding electromagnetic potential permitting separation of variables.

KW - (2 + 1)-dimensional Dirac equation

KW - separation of variables

KW - symmetry operators

UR - http://www.scopus.com/inward/record.url?scp=85044793408&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85044793408&partnerID=8YFLogxK

U2 - 10.1142/S0219887818500858

DO - 10.1142/S0219887818500858

M3 - Article

AN - SCOPUS:85044793408

VL - 15

JO - International Journal of Geometric Methods in Modern Physics

JF - International Journal of Geometric Methods in Modern Physics

SN - 0219-8878

IS - 5

M1 - 1850085

ER -