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

22nd 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: Dirac equations;    Gauge fields;    Integration method;    Invariant matrices;    Invariant metric;    Non-commutative;    Symmetry groups;    Yang-Mills fields;   

Others  :  https://iopscience.iop.org/article/10.1088/1742-6596/563/1/012004/pdf
DOI  :  10.1088/1742-6596/563/1/012004

来源: IOP

【 摘 要 】

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× S2by a noncommutative integration method.