### 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 |
---|---|

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 |

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### Keywords

- Dirac equation
- noncommutative integration
- symmetry algebra

### ASJC Scopus subject areas

- Physics and Astronomy(all)

### Cite this

*Russian Physics Journal*,

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

**Noncommutative Integration and Symmetry Algebra of the Dirac Equation on the Lie Groups.** / Breev, A. I.; Mosman, E. A.

Research output: Contribution to journal › Article

*Russian Physics Journal*, vol. 59, no. 8, pp. 1153-1163. https://doi.org/10.1007/s11182-016-0885-6

}

TY - JOUR

T1 - Noncommutative Integration and Symmetry Algebra of the Dirac Equation on the Lie Groups

AU - Breev, A. I.

AU - Mosman, E. A.

PY - 2016/12/1

Y1 - 2016/12/1

N2 - 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.

AB - 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.

KW - Dirac equation

KW - noncommutative integration

KW - symmetry algebra

UR - http://www.scopus.com/inward/record.url?scp=85002180261&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85002180261&partnerID=8YFLogxK

U2 - 10.1007/s11182-016-0885-6

DO - 10.1007/s11182-016-0885-6

M3 - Article

VL - 59

SP - 1153

EP - 1163

JO - Russian Physics Journal

JF - Russian Physics Journal

SN - 1064-8887

IS - 8

ER -