一阶微分算子的酉等价类
Unitarily Equivalent Classes of First Order Differential Operators
摘要：
基于同一向量场的一类非齐次微分算子的元素，当被视为作用在适当的希尔伯特空间上时，被证明是彼此同构的。指出用齐次算子代替非齐次算子就是适当地改变流形中的体积元。重点讨论了对称算符和相应的量子动量观测量的情形。
英文摘要：
The elements of the class of non-homogeneous differential operators which are based on the same vector field, when viewed as acting on appropriate Hilbert spaces, are shown to be isomorphic to each other. It shown that the replacement of a non-homogeneous operator by a homogeneous one amouts to appropriately changing the volume element in the manifold. An emphasize is given to the case of symmetric operators and the corresponding quantum momentum observables.
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。
