DFG-NSF: investigations on physical implications of canonical quantum gravity

量子力学与广义相对论的统一是理论物理的主要基本问题之一。但是，量子和引力的结合面临着许多挑战性的障碍。在量子引力的正则方法中，如圈量子引力，主要的开放问题是以所谓的量子爱因斯坦方程的形式来表达量子动力学，沿着的量子化过程如何影响动力学，从而产生物理意义。所有基于正则量子引力的模型，包括环量子宇宙学，它已经成功地解决了各种奇异性，并预测了宇宙微波背景中的潜在特征，都以一种或另一种形式面临上述问题，以产生可靠的物理图像。这个提议的主要目标是使用基于时钟和狄拉克观测量的关系形式主义来解决和获得对这些基本问题的见解，该关系形式主义允许在广义相对论的背景下定义规范不变量。利用已有的量子爱因斯坦方程模型和经典宇宙学微扰理论的结果，该建议旨在探索这些方法在宇宙学背景下的经典和量子水平上的分支，包括对宇宙学微扰理论的影响。这项研究的结果一方面将在更接近全圈量子引力的更一般的环境中测试量子宇宙学模型中迄今为止可用的预测，另一方面将对量子化选择和规范固定影响物理预测的方式产生有价值的见解。

The unification of quantum mechanics and general relativity is one of the main fundamental problems of theoretical physics. But, the marriage of quantum and gravity faces many challenging hurdles. In the canonical approaches to quantum gravity, such as loop quantum gravity, the main open problems are to formulate the quantum dynamics in form of so called quantum Einstein equations, along with how does the quantization procedure affects the dynamics, and hence physical implications. All models based on canonical quantum gravity, including loop quantum cosmology which has successfully led to resolution of various singularities and predicts potential signatures in the cosmic microwave background, face above problems in one form or another to yield a reliable physical picture. The main goal of this proposal is to address and gain insights on these fundamental issues using the relational formalism based on clocks and Dirac observables that allows to define gauge invariant quantities in the context of general relativity. Using already existing models for the quantum Einstein equations and results in canonical cosmological perturbation theory, this proposal aims to explore ramifications of these methods in the cosmological setting, both at classical and quantum level, including implications for cosmological perturbation theory. Results from this research on the one hand will test so far available predictions in quantum cosmological models in a more general setting which is closer to full loop quantum gravity, and on the other hand yield valuable insights on the way quantization choices and gauge fixing affect physical predictions.