Non-factorizable separable systems and higher-order symmetries of the Dirac operator

M. Fels, N. Kamran
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引用次数: 27

Abstract

It is shown that there exist separable systems for the Dirac operator on four-dimensional lorentzian spin manifolds that are not factorizable in the sense of Miller. The symmetry operators associated to these new separable systems are of higher order than the Dirac operator. They are characterized in the second-order case in terms of quadratic first integrals of the geodesic flow satisfying additional invariant conditions.
不可分解可分离系统与Dirac算子的高阶对称性
证明了四维洛伦兹自旋流形上的狄拉克算子存在米勒意义上不可因式分解的可分离系统。与这些新分离系统相关的对称算子比狄拉克算子具有更高阶。在二阶情况下,它们被描述为满足附加不变条件的测地线流的二次一阶积分。
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