### Abstract

We consider the Dirac equation with an external Yang-Mills gauge field in a homogeneous space with an invariant metric. The Yang-Mills fields for which the motion group of the space serves as the symmetry group for the Dirac equation are found by comparison of the Dirac equation with an invariant matrix differential operator of the first order. General constructions are illustrated by the example of de Sitter space. The eigenfunctions and the corresponding eigenvalues for the Dirac equation are obtained in the space R<sup>2</sup> × S<sup>2</sup> by a noncommutative integration method.

Original language | English |
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Article number | 012004 |

Journal | Journal of Physics: Conference Series |

Volume | 563 |

Issue number | 1 |

DOIs | |

Publication status | Published - 26 Nov 2014 |

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### ASJC Scopus subject areas

- Physics and Astronomy(all)

### Cite this

**Yang-Mills gauge fields conserving the symmetry algebra of the Dirac equation in a homogeneous space.** / Breev, A. I.; Shapovalov, Aleksandr Vasilievich.

Research output: Contribution to journal › Article

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TY - JOUR

T1 - Yang-Mills gauge fields conserving the symmetry algebra of the Dirac equation in a homogeneous space

AU - Breev, A. I.

AU - Shapovalov, Aleksandr Vasilievich

PY - 2014/11/26

Y1 - 2014/11/26

N2 - We consider the Dirac equation with an external Yang-Mills gauge field in a homogeneous space with an invariant metric. The Yang-Mills fields for which the motion group of the space serves as the symmetry group for the Dirac equation are found by comparison of the Dirac equation with an invariant matrix differential operator of the first order. General constructions are illustrated by the example of de Sitter space. The eigenfunctions and the corresponding eigenvalues for the Dirac equation are obtained in the space R2 × S2 by a noncommutative integration method.

AB - We consider the Dirac equation with an external Yang-Mills gauge field in a homogeneous space with an invariant metric. The Yang-Mills fields for which the motion group of the space serves as the symmetry group for the Dirac equation are found by comparison of the Dirac equation with an invariant matrix differential operator of the first order. General constructions are illustrated by the example of de Sitter space. The eigenfunctions and the corresponding eigenvalues for the Dirac equation are obtained in the space R2 × S2 by a noncommutative integration method.

UR - http://www.scopus.com/inward/record.url?scp=84938520932&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84938520932&partnerID=8YFLogxK

U2 - 10.1088/1742-6596/563/1/012004

DO - 10.1088/1742-6596/563/1/012004

M3 - Article

VL - 563

JO - Journal of Physics: Conference Series

JF - Journal of Physics: Conference Series

SN - 1742-6588

IS - 1

M1 - 012004

ER -