量化三柱问题
Quantised Three-Pillar Problem
摘要：
本文研究了量子力学系统，当一个量子化的经典力学配置所描述的欠定系统的方程。具体地说，我们考虑著名的问题，在经典力学中，梁是由三个相同的刚性支柱。对于这个问题，不可能唯一地计算每个支柱提供的力。然而，如果用弹簧代替支柱，则力是唯一确定的。当弹性常数趋于无穷大时，三柱问题及其相关的不确定性在极限中恢复。在本文中，弹簧版本的问题被量化为一个约束动力系统。然后，它表明，作为弹性常数变得很大，量子模拟的模糊性重新出现作为一种量子异常。
英文摘要：
This paper examines the quantum mechanical system that arises when one quantises a classical mechanical configuration described by an underdetermined system of equations. Specifically, we consider the well-known problem in classical mechanics in which a beam is supported by three identical rigid pillars. For this problem it is not possible to calculate uniquely the forces supplied by each pillar. However, if the pillars are replaced by springs, then the forces are uniquely determined. The three-pillar problem and its associated indeterminacy is recovered in the limit as the spring constant tends to infinity. In this paper the spring version of the problem is quantised as a constrained dynamical system. It is then shown that as the spring constant becomes large, the quantum analog of the ambiguity reemerges as a kind of quantum anomaly.
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