Weyl代数的模聚合表示
Modular polymer representations of the Weyl algebra
摘要：
量子引力的关键概念挑战之一是理解量子理论应该如何修改时空的概念。研究这个问题的一种方法是研究薛定谔量子力学的替代理论。受圈量子引力启发的聚合物表示法可以被理解为捕捉离散空间几何的特征。另一方面，模表示通过长度尺度具有位置和动量极化的内在统一。在这篇文章中，我们介绍了Weyl代数的模聚合表示，其中位置和动量都不存在作为一个定义良好的操作。作为不等价的表示，它们是描述新物理学的候选者。我们通过研究谐振子的动力学作为一个例子来说明这一点，最终将这种表示应用于量子宇宙学的前景。
英文摘要：
One of the key conceptual challenges in quantum gravity is to understand how quantum theory should modify the very notion of spacetime. One way to investigate this question is to study the alternatives to Schrödinger quantum mechanics. The polymer representation, inspired by loop quantum gravity, can be understood as capturing features of discrete spatial geometry. The modular representation, on the other hand, has a built-in unification of position and momentum polarizations via a length scale. In this paper, we introduce the modular polymer representations of the Weyl algebra, in which neither position nor momentum exists as a well-defined operator. As inequivalent representations, they are candidates for describing new physics. We illustrate this by studying the dynamics of the harmonic oscillator as an example, with the prospect of eventually applying this representation to quantum cosmology.
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