Effective Descriptions of Quantum Gravity and Cosmology

广义相对论和量子力学是支配时空和基本粒子基础物理学的两大理论。然而，目前还不知道如何将它们结合起来形成一个一致的量子引力理论。因此，诸如大爆炸的最初阶段或黑洞的核心等迷人的现象仍然超出了我们目前的理解范围。本项目研究了广义相对论和量子力学相关的广泛系统。主要的兴趣是通过允许人们通过近似推导物理含义的方法，并使用结果来指导量子引力的发展。对大爆炸和黑洞的应用通常会得出引起公众兴趣的结论。相关方法也可以用于不涉及广义相对论的系统，在那里它们可能有助于解决技术问题或以一种新的方式传达结果，例如支持量子力学的教学。该项目的目的是介绍和评估新的方法，以系统地分析一组候选量子引力理论的物理含义，基于规范量子化。在整个物理学中，有效的理论提供了一个强大的工具来推导潜在的可观察现象，这些理论为经典方程提供了量子修正。与量子态方程相比，这样的系统可以更容易地进行分析或数值评估，因此是发现新现象的更直接的来源。虽然推导有效方程的标准技术不适用于经典量子引力，但存在一种适用于经典量子理论的一般方案（由PI引入），并在本项目中用于解决量子引力的主要问题。它为在量子引力的广泛背景下评估物理现象的长期计划提供了基础。这样一个系统的推导将有可能把以前在简化模型中发现的效应建立在坚实的基础上，揭示新的现象，并提供可靠的预测。研究结果将用于将该理论与其他候选量子引力理论进行比较，并有可能在不同方法之间进行富有成效的思想和技术转移。

General relativity and quantum mechanics are the two major theories that govern fundamental physics, of space-time and of elementary particles. However, it is not known how they could be combined to a consistent theory of quantum gravity. Fascinating phenomena such as the very first stages of the big bang or the cores of black holes therefore remain out of the reach of our current understanding. This project investigates a wide range of systems in which both general relativity and quantum mechanics are relevant. The main interest is given by methods that allow one to derive physical implications by approximations, and to use the results to guide the developments of quantum gravity. Applications to the big bang and black holes often lead to conclusions that capture the interest of the general public. Related methods can also be used in systems not involving general relativity, where they may help to solve technical questions or to communicate results in a new way, supporting for instance the teaching of quantum mechanics.The objective of this project is to introduce and evaluate new methods for a systematic analysis of physical implications of one set of candidate theories of quantum gravity, based on canonical quantization. Throughout physics, a powerful tool to derive potentially observable phenomena is given by effective theories which provide quantum corrections to the classical equations. Such systems can more easily be evaluated, analytically or numerically, than equations for quantum states and thus are more direct sources for the discovery of new phenomena. While standard techniques to derive effective equations do not apply to canonical quantum gravity, a general scheme applicable to canonical quantum theories exists (introduced by the PI) and is used in this project to address the main problems of quantum gravity. It provides the basis for a long-term program evaluating physical phenomena in the broad context of quantum gravity. Such a systematic derivation will make it possible to put effects found previously in simplified models on a firm footing, uncover new phenomena and provide reliable predictions. Results will be used to compare the theory with other candidates of quantum gravity, with the potential of a fruitful transfer of ideas and techniques between the approaches.