Understanding some physical features of quantum gravity

物理学家李·斯莫林在他的《三条通往地心引力的道路》一书中写道：“毕竟，原子确实会下落，所以引力和量子之间的关系对自然界来说不是问题。”然而，广义相对论和量子理论的具体统一仍然是一个悬而未决的问题。 我的研究计划旨在更好地理解量子引力机制，它基于所谓的“循环量子引力”(LQG)和“自旋泡沫”(SF)框架，这两个框架基于应用于广义相对论的两种不同的量子化技术。LQG框架源于正则量化方案，而SF模型是使用路径积分量化来构建的。 我的长期目标是定义一个一致的量子引力理论，从中提取物理预测。最近宣布的中子星碰撞观测标志着多信使天文学的开始(引力波和电磁现象，如伽马射线暴可以在同一事件上观察到)，这可能为量子引力现象打开新的令人兴奋的实验窗口。为了做出物理预测，例如，可以通过费米伽马射线太空望远镜进行检查，人们需要了解如何引入物质及其与LQG/SF框架的相互作用。同样在经验上，过去几十年的宇宙学数据强烈表明，我们的宇宙具有正的宇宙学常数10-52m-2。因此，建立一个具有不消失的宇宙常数的量子引力理论至关重要。具体地说，短期内，我想： -通过引入不消失的宇宙常数和物质来改进LQG和SF框架的定义。 -以更加数学一致的方式定义四维SF模型。 这些都是非常具有挑战性的目标，需要技术创新和使用许多不同的数学方法。我的研究将使用3D引力作为一个框架，其中可以比较几种方法，将借用非对易几何的工具，开发新的LQG离散化方案，并将SF框架与更标准的量子场论框架联系起来。 我的研究小组将研究与LQG和SF模型相关的问题，但也会研究非对易几何、量子场论以及数学物理。我和我的团队发现的结果将为量子引力机制提供新的物理预测机会。 量子引力是一个吸引优秀学生并提供令人兴奋的扩展主题的领域。这大大增加了选择STEM科目的学生总数，从而影响了加拿大的研究和开发部门。我的计划将为三名数学学生和三名博士生提供培训，并为他们在学术界或私营部门担任高素质职位做好准备。

“After all, atoms do fall, so the relationship between gravity and quantum is not a problem for nature,” stated physicist Lee Smolin in his book Three Roads to Gravity. However, the concrete unification of General Relativity and Quantum Theory is still an open issue. My research program, which aims to better understand the quantum gravity regime, is based on the so-called “Loop Quantum Gravity” (LQG) and “Spinfoam” (SF) frameworks, which are based on the use of two different quantization techniques applied to general relativity. The LQG framework arises from the canonical quantization scheme, whereas SF models are constructed using the path integral quantization. My long-term objective is to define a consistent theory of quantum gravity, from which physical predictions can be extracted. Recent announcements on the neutron stars collision observation marked the beginning of multi-messenger astronomy (gravitational waves and electromagnetic phenomena such as gamma ray bursts can be observed on a same event), which could open new exciting experimental windows for quantum gravity phenomena. To make physical predictions, which could be checked by the Fermi Gamma-ray Space Telescope for instance, one needs to understand how to introduce matter and its interactions with the LQG/SF framework. Also empirically, the cosmological data of the past decades strongly suggests that our universe has a positive cosmological constant 10-52m-2. It is therefore crucial to build a theory of quantum gravity with a non-vanishing cosmological constant. Concretely, in the short term, I want to: - Improve the definition of the LQG and SF frameworks by introducing a non-vanishing cosmological constant and matter. - Define a four-dimensional SF model in a more mathematically consistent way. These are very challenging aims, which require technical innovations and the use of many different mathematical approaches. My research will use 3d gravity as a framework where several approaches can be compared, will borrow tools from non-commutative geometry, exploit new discretization schemes for LQG and relate the SF framework to the more standard quantum field theory framework. My research group will investigate issues associated with LQG and SF models but also in non-commutative geometry, quantum field theory as well as mathematical physics. The results found by my team and I will provide new opportunities to make physical predictions for the quantum gravity regime. Quantum Gravity is a field that attracts excellent students and provides exciting outreach topics. This contributes greatly to the total number of students choosing STEM subjects, and consequently impacts the research and development sector in Canada. My program will provide training for three MMath students and three PhD students and will prepare them to work in academia or in the private sector in highly qualified positions.