广义向心力定律与二维曲面约束运动的量子化
Generalized Centripetal Force Law and Quantization of Motion Constrained on 2D Surfaces
摘要：
当粒子在三维欧氏空间中的二维曲面f（x）=0上运动时，在约束运动的狄拉克正则量子化方案中，几何动量和几何势是同时容许的。在我们的方法中，除了利用基本的对称性[x，x]_{D}，[x，p]_{D}和[p，p]_{D}之外，还利用了经典括号[x，H]_{D}和[p，H]_{D}所表示的对称性，其中下标D代表Dirac括号。二维曲面上质点的广义向心力定律p=[p，H]_{D}起着关键作用，曲面上一点的力与该点的曲率之间没有简单的关系，这与曲线上的运动形成了鲜明的对比。
英文摘要：
For a particle moves on a 2D surface f(x)=0 embedded in 3D Euclidean space, the geometric momentum and potential are simultaneously admissible within the Dirac canonical quantization scheme for constrained motion. In our approach, not the full scheme but the symmetries indicated by classical brackets [x,H]_{D} and [p,H]_{D} in addition to the fundamental ones [x,x]_{D}, [x,p]_{D} and [p,p]_{D} are utilized, where the subscript D stands for the Dirac bracket. The generalized centripetal force law p=[p,H]_{D} for particle on the 2D surface play the key role, and there is no simple relationship between the force on a point of the surface and its curvatures of the point, in sharp contrast to the motion on a curve.
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