一类自然哈密顿量首次积分构造方法的推广及量子化的一些注记
Generalizations of a method for constructing first integrals of a class of natural Hamiltonians and some remarks about quantization
摘要：
在以前的论文中，我们确定了存在一类自然哈密顿量的必要和充分条件与非平凡的第一次积分的任意高次的动量。这些哈密顿算子被刻画为n维哈密顿算子在常曲率（伪）黎曼流形Q上的（n+1）维扩张。在本文中，我们推广的方法在各个方向，我们得到了一个明确的第一积分的表达式，持有更一般的情况下的Hamilton Poisson流形，并显示如何建设上述是可能的存在Q上的特定的共形Killing张量，或等价地，特定的共形主对称的测地线方程。最后，我们考虑了这些第一积分的Laplace-Beltrami量子化的问题时，他们是第二次。
英文摘要：
In previous papers we determined necessary and sufficient conditions for the existence of a class of natural Hamiltonians with non-trivial first integrals of arbitrarily high degree in the momenta. Such Hamiltonians were characterized as (n+1)-dimensional extensions of n-dimensional Hamiltonians on constant-curvature (pseudo-)Riemannian manifolds Q. In this paper, we generalize that approach in various directions, we obtain an explicit expression for the first integrals, holding on the more general case of Hamiltonians on Poisson manifolds, and show how the construction of above is made possible by the existence on Q of particular conformal Killing tensors or, equivalently, particular conformal master symmetries of the geodesic equations. Finally, we consider the problem of Laplace-Beltrami quantization of these first integrals when they are of second-degree.
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。
