Continuum limit, dynamics and holography in quantum gravity

“空间和时间的本质是什么？”这个问题推动了几个世纪以来物理学的发展。20世纪初，物理学因两次不同的范式转变而发生了革命性的变化：一方面，爱因斯坦认为空间和时间是一个统一的、动态的物体，它描述了引力；另一方面，是量子理论的发明，它规定了基本物质固有的模糊性。******到20世纪末，很明显，这两种理论，分开来看，都预言了它们自己的灭亡：爱因斯坦的引力理论预言了物质坍缩成黑洞，越来越多的物质坍缩成一个时空奇点。描述基本物质相互作用的量子理论导致无穷大，因此在非常小的距离上不一致。因此，我们需要一种量子引力理论，用真正的量子时空取代平滑时空，而平滑时空是20世纪物理学的基础。随着时空本身成为一个模糊的对象，这样的理论将再次彻底改变我们对空间和时间的理解。******目前，我们有很多方法来研究量子引力理论，但它们都面临着一个关键的挑战：证明量子时空确实会导致平滑时空，就像我们在日常世界中所经历的那样。只有这样，我们才能接受一个给定的方法作为量子引力理论。这将是本研究项目要解决的主要问题。******这是一项非常困难的任务，因为它需要前所未有的数量级的桥梁。这可以比作从氢原子和氧原子之间的相互作用推导出水的流体动力学。然而，有一些令人兴奋的事态发展使这项任务得以实现。最重要的是，这使我能够开发一个重整化框架，适用于非微扰量子引力方法，这导致了第一个解决连续体极限的数值算法的构建。本研究计划将扩展现有的分析和数值工具，并利用这些工具来提取量子引力模型的连续统极限。******这项研究将极大地促进我们对量子引力模型中编码的动力学的掌握。而不是专注于建立特定的量子引力模型，将开发的方法将允许统一的处理和推导普遍以及模型依赖的预测。这将是推导物理预测和构建改进模型的关键，这将帮助我们解开量子时空的概念。******量子引力研究吸引了优秀的学生，并提供了令人兴奋的材料。这将增加选择STEM学科的学生，并使他们保持动力，从而帮助加拿大保持和扩大其在研发领域的优势。

“What is the nature of space and time?” This is a question that has advanced the development of physics through the centuries. Physics was revolutionized at the beginning of the 20th century by two separate paradigm shifts: On the one hand, Einstein's vision of space and time as a unified and dynamical object that describes the gravitational force; on the other, the invention of quantum theory that prescribes an inherent fuzziness to fundamental matter. ******By the end of the 20th century, it became clear that both theories, taken separately, predict their own demise: Einstein's theory of gravitation predicts the collapse of matter to black holes, that crash more and more matter into a spacetime singularity. Quantum theory, describing the fundamental matter interactions, leads to infinities and therefore inconsistencies at very small distances. We need therefore a theory of quantum gravity that replaces smooth space time, on which 20th century physics is based, with a truly quantum space time. With space time itself becoming a fuzzy object, such a theory will again revolutionize our understanding of space and time. ******Currently, we have a number of approaches to a quantum theory of gravity, but they all face a key challenge: to show that quantum space time does lead to smooth space time, as we experience it in our everyday world. Only then can we accept a given approach as a theory of quantum gravity. This will be the main issue tackled by this research program. ******It is a very difficult task as it requires the bridging of an unprecedented number of magnitudes. It can be compared to deriving the hydrodynamics of water from the interactions between the hydrogen and oxygen atoms. There have been, however, a number of exciting developments which bring this task into reach. Most importantly, these allowed me to develop a framework of renormalization, applicable to non-perturbative quantum gravity approaches, which led to the construction of first numerical algorithms to tackle the continuum limit. This research program will expand the current analytical and numerical tools and use these to extract the continuum limit of quantum gravity models. ******This research will significantly advance our grasp on the dynamics encoded in quantum gravity models. Instead of being focussed on building particular models of quantum gravity, the methods that will be developed will allow a unified treatment and the derivation of universal as well as model dependent predictions.***This will be key to derive physical predictions and to construct improved models, which will help us to unravel the notion of quantum space time. ******Quantum gravity research attracts excellent students and provides outreach efforts with exciting material. This will increase students choosing STEM subjects and keeps them motivated, which will, in turn help Canada to keep and expand its edge in the research and development sector.