二维球面Monge参数化中的几何动量
Geometric momentum in the Monge parametrization of two dimensional sphere
摘要：
一个二维表面可以看作是三维壳，其厚度与整个系统的尺寸相比可以忽略不计。表面上的量子力学可以先在体中表述，然后取消失厚度的极限。将原来定义在块体上的梯度算子和拉普拉斯算子收敛到曲面上的几何算子，得到了所谓的几何动量和几何势。在二维球面上，明确地探讨了Monge参数化中的几何动量。利用狄拉克的第二类约束运动理论来解释交换子[ x_{i}，p_{j} ]= iPDMATHABMO（δ_{ij}- x_{i} x_{j} /r^2）而不是不再成立的[ x_{i}，p_{j} ]=i \hbar δ_{ij}.这种几何动量在参数变换下具有几何不变性，并且是自伴的。
英文摘要：
A two dimensional surface can be considered as three dimensional shell whose thickness is negligible in comparison with the dimension of the whole system. The quantum mechanics on surface can be first formulated in the bulk and the limit of vanishing thickness is then taken. The gradient operator and the Laplace operator originally defined in bulk converges to the geometric ones on the surface, and the so-called geometric momentum and geometric potential are obtained. On the surface of two dimensional sphere the geometric momentum in the Monge parametrization is explicitly explored. Dirac's theory on second-class constrained motion is resorted to for accounting for the commutator [x_{i},p_{j}]=i \hbar(δ_{ij}-x_{i}x_{j}/r^2) rather than [x_{i},p_{j}]=i\hbarδ_{ij} that does not hold true any more. This geometric momentum is geometric invariant under parameters transformation, and self-adjoint.
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