论文标题
Weyl代数的模块化聚合物表示
Modular polymer representations of the Weyl algebra
论文作者
论文摘要
量子重力的关键概念挑战之一是了解量子理论应如何修改时空的概念。研究这个问题的一种方法是研究Schrödinger量子力学的替代方法。受环量子重力启发的聚合物表示，可以理解为捕获离散空间几何形状的特征。另一方面，模块化表示通过长度比例内置了位置和动量极化的内置统一。在本文中，我们介绍了Weyl代数的模块化聚合物表示，其中位置和动量都不存在作为定义明确的操作员。作为不等式的表示，它们是描述新物理学的候选人。我们通过研究谐波振荡器的动力学来说明这一点，以最终将此表示形式应用于量子宇宙学。
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.
