### Abstract

The algebra of first-order symmetry operators of the Dirac equation on four-dimensional Lie groups with right-invariant metric is investigated. It is shown that the algebra of symmetry operators is in general not a Lie algebra. Noncommutative reduction mediated by spin symmetry operators is investigated. For the Dirac equation on the Lie group SO(2,1) a parametric family of particular solutions obtained by the method of noncommutative integration over a subalgebra containing a spin symmetry operator is constructed.

Original language | English |
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Pages (from-to) | 1153-1163 |

Number of pages | 11 |

Journal | Russian Physics Journal |

Volume | 59 |

Issue number | 8 |

DOIs | |

Publication status | Published - 1 Dec 2016 |

### Keywords

- Dirac equation
- noncommutative integration
- symmetry algebra

### ASJC Scopus subject areas

- Physics and Astronomy(all)

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## Cite this

Breev, A. I., & Mosman, E. A. (2016). Noncommutative Integration and Symmetry Algebra of the Dirac Equation on the Lie Groups.

*Russian Physics Journal*,*59*(8), 1153-1163. https://doi.org/10.1007/s11182-016-0885-6