论文标题
量子几何II：循环量子重力的数学三维量子重力
Quantum Geometry II : The Mathematics of Loop Quantum Gravity Three dimensional quantum gravity
论文作者
论文摘要
循环量子重力是一种物理理论，旨在统一一般相对论和量子力学。它非常重视一般的相对论，并通过定量对其进行修改。一般相对论在几何学方面描述了重力。因此，量化这种理论必须等同于量化几何形状，这就是循环量子重力所做的。这听起来也像是一项数学任务。这就是为什么在本文中我们将介绍环量子重力的数学。我们将从数学家的角度做到这一点。本文旨在作为物理和数学研究生的循环量子重力介绍。在这项工作中，我们将把自己限制在三维案例中。
Loop quantum gravity is a physical theory which aims at unifying general relativity and quantum mechanics. It takes general relativity very seriously and modifies it via a quantisation. General relativity describes gravity in terms of geometry. Therefore, quantising such theory must be equivalent to quantising geometry and that is what loop quantum gravity does. This sounds like a mathematical task as well. This is why in this paper we will present the mathematics of loop quantum gravity. We will do it from a mathematician point of view. This paper is intended to be an introduction to loop quantum gravity for postgraduate students of physics and mathematics. In this work we will restrict ourselves to the three dimensional case.
