环面上的量子力学对偶
Quantum-Mechanical Dualities on the Torus
摘要：
在只允许一个复可微结构的经典相空间上，在从给定真空中创造量子的创造算符的选择上没有不确定性。在这些情况下，量子的概念是普遍的，即，在经典相空间上与观测器无关。在量子力学的所有标准应用中都是如此。然而，最近的发展表明，量子的概念可能不是普遍的。对于基本量子概念不一致的观察者之间的变换称为对偶。经典相空间允许一个以上的复微分结构，从而提供了一个自然的框架，研究对偶量子力学。作为一个例子，我们量子化了一个相空间为环面的经典力学，并明确地证明了它具有对偶性。
英文摘要：
On classical phase spaces admitting just one complex-differentiable structure, there is no indeterminacy in the choice of the creation operators that create quanta out of a given vacuum. In these cases the notion of a quantum is universal, i.e., independent of the observer on classical phase space. Such is the case in all standard applications of quantum mechanics. However, recent developments suggest that the notion of a quantum may not be universal. Transformations between observers that do not agree on the notion of an elementary quantum are called dualities. Classical phase spaces admitting more than one complex-differentiable structure thus provide a natural framework to study dualities in quantum mechanics. As an example we quantise a classical mechanics whose phase space is a torus and prove explicitly that it exhibits dualities.
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