运动群$G_3$传递作用于时空的零子曲面时Klein-Gordon-Fock方程的对称算子代数
Algebra of the symmetry operators of the Klein-Gordon-Fock equation for the case when groups of motions $G_3$ act transitively on null subsurfaces of spacetime
摘要：
对于在时空流形中的外电磁场中运动的带电试验粒子，在三参数运动群传递的各向同性（零）超曲面上，给出了Hamilton-Jacobi和Klein-Gordon-Fock方程的对称算子代数.我们已经找到了所有允许存在这种代数的电磁场。我们证明了自由Hamilton-Jacobi和Klein-Gordon-Fock方程的容许场不使对称算子代数变形。这些结果完成了容许电磁场的分类，其中Hamilton-Jacobi和Klein-Gordon-Fock方程允许运动积分代数同构于$r$ -时空流形运动的参数群的算子代数，如果$(r \leq 4)$。
英文摘要：
The algebras of the symmetry operators for the Hamilton-Jacobi and Klein-Gordon-Fock equations are found for a charged test particle moving in an external electromagnetic field in a spacetime manifold, on the isotropic (null) hypersurface of which a three-parameter groups of motions act transitively.on the isotropic (null) hypersurface of which a three-parameter groups of motions act transitively. We have found all admissible electromagnetic fields for which such algebras exist. We have proved that an admissible field does not deform the algebra of symmetry operators for the free Hamilton-Jacobi and Klein-Gordon-Fock equations. The results complete the classification of admissible electromagnetic fields in which the Hamilton-Jacobi and Klein-Gordon-Fock equations admit algebras of motion integrals that are isomorphic to the algebras of operators of $r$-parametric groups of motions of spacetime manifolds if $(r \leq 4)$.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
