The Dirac equation in an external electromagnetic field: symmetry algebra and exact integration

23rd International Conference on Integrable Systems and Quantum Symmetries

Breev, A.I.^1,2 ; Shapovalov, A.V.^1,2

Department of Theoretical Physics, Tomsk State University, Tomsk

634050, Russia^1

Department of Higher Mathematics and Mathematical Physics, Tomsk Polytechnic University, Tomsk

634050, Russia^2

关键词: Crossed electric and magnetic fields;    Dirac equations;    Exact integration;    External electromagnetic field;    Method of separation of variables;    Non local symmetries;    Non-commutative;    Separation of variables;   

Others  :  https://iopscience.iop.org/article/10.1088/1742-6596/670/1/012015/pdf
DOI  :  10.1088/1742-6596/670/1/012015

来源: IOP

【 摘 要 】

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.