论文标题
klein-gordon-fock方程的对称运算符的代数，当时$ g_3 $在null spaceTime的无子侧面上行动$ g_3 $
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
论文作者
论文摘要
在时空歧管中的外部电磁场中移动的电荷测试粒子，在各向同性（NULL）高度表面上在外部电磁场中移动的充电测试粒子的对称算子的代数是在外部电磁场中移动的电荷测试粒子方程的代数。采取传统行动。我们发现存在此类代数的所有可接受的电磁场。我们已经证明，免费的汉密尔顿 - 雅各比和克莱因·戈登 - 库克方程的对称操作员的代数不会变形。结果完成了可允许的电磁场的分类，其中汉密尔顿 - 雅各比和克莱因 - 戈登 - 库克方程允许运动积分代数代数，这些代数对$ r $ r $ r $ r $ r $参数的代数是$ r $ r $ - 比起$ r $ - spaceTime commetric of Spacetime compacters formolds if $（r \ r \ leq 4）$的代数。
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 $(r \leq 4)$.
