### Abstract

Integration of the Dirac equation with an external electromagnetic field is explored in the framework of the method of separation of variables and of the method of noncommutative integration. We have found a new type of solutions that are not obtained by separation of variables for several external electromagnetic fields. We have considered an example of crossed electric and magnetic fields of a special type for which the Dirac equation admits a nonlocal symmetry operator.

Original language | English |
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Article number | 012015 |

Journal | Journal of Physics: Conference Series |

Volume | 670 |

Issue number | 1 |

DOIs | |

Publication status | Published - 25 Jan 2016 |

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### ASJC Scopus subject areas

- Physics and Astronomy(all)

### Cite this

**The Dirac equation in an external electromagnetic field : Symmetry algebra and exact integration.** / Breev, A. I.; Shapovalov, Aleksandr Vasilievich.

Research output: Contribution to journal › Article

}

TY - JOUR

T1 - The Dirac equation in an external electromagnetic field

T2 - Symmetry algebra and exact integration

AU - Breev, A. I.

AU - Shapovalov, Aleksandr Vasilievich

PY - 2016/1/25

Y1 - 2016/1/25

N2 - Integration of the Dirac equation with an external electromagnetic field is explored in the framework of the method of separation of variables and of the method of noncommutative integration. We have found a new type of solutions that are not obtained by separation of variables for several external electromagnetic fields. We have considered an example of crossed electric and magnetic fields of a special type for which the Dirac equation admits a nonlocal symmetry operator.

AB - Integration of the Dirac equation with an external electromagnetic field is explored in the framework of the method of separation of variables and of the method of noncommutative integration. We have found a new type of solutions that are not obtained by separation of variables for several external electromagnetic fields. We have considered an example of crossed electric and magnetic fields of a special type for which the Dirac equation admits a nonlocal symmetry operator.

UR - http://www.scopus.com/inward/record.url?scp=84962385236&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84962385236&partnerID=8YFLogxK

U2 - 10.1088/1742-6596/670/1/012015

DO - 10.1088/1742-6596/670/1/012015

M3 - Article

AN - SCOPUS:84962385236

VL - 670

JO - Journal of Physics: Conference Series

JF - Journal of Physics: Conference Series

SN - 1742-6588

IS - 1

M1 - 012015

ER -