Quantum aspects of different formulations of general relativity

广义相对论描述了我们目前对引力的最好理解，它可以用不同的变量和不同的经典作用来定义。虽然这些不同的公式在经典解和预测上是一致的，但它们是否具有相同的量子行为却不太清楚。例如，用（自对偶）自旋连接代替度规作为基本变量可以导致环量子引力的构建，这是一个在原始度规公式中不存在的理论。本项目将研究广义相对论的各种公式，特别是那些自旋连接起基本作用的公式，并比较它们的量子特性。重点将放在对称宇宙学模型上，其中量化可以明确地实现，并且没有标准量子引力的病理。

The theory of general relativity which describes our current best understanding of gravity can be defined in terms of different variables and different classical actions. While these different formulations agree in their classical solutions and predictions, it is much less clear whether they have the same quantum behaviour. For example replacing the metric by a (self-dual) spin connection as a fundamental variable can lead to the construction of loop quantum gravity, a theory that does not exist in the original metric formulation. This project will study various formulations of general relativity, in particular those in which the spin connection plays a fundamental role, and compare their quantum properties. A focus will be on symmetric cosmological models where quantisation can be achieved unambiguously and without the pathologies of standard quantum gravity.