共形不变Laplace-Beltrami算子与因子序
The conformally invariant Laplace-Beltrami operator and factor ordering
摘要：
在量子力学中，单个粒子的动能项通常写成拉普拉斯-贝尔特拉米算符的形式。该算子是经典动能的因子序。我们调查其他相对简单的因子排序，并表明，{ \it唯一}的其他解决方案的共形平坦的度量是共形不变的Laplace-Beltrami算子。对于非共形平坦度量，这种类型的因子排序失败，只有一个术语，给出共形不变的拉普拉斯-贝尔特拉米算子。
英文摘要：
In quantum mechanics the kinetic energy term for a single particle is usually written in the form of the Laplace-Beltrami operator. This operator is a factor ordering of the classical kinetic energy. We investigate other relatively simple factor orderings and show that the {\it only} other solution for a conformally flat metric is the conformally invariant Laplace-Beltrami operator. For non-conformally-flat metrics this type of factor ordering fails, by just one term, to give the conformally invariant Laplace-Beltrami operator.
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