Non-locality of Quantum geometry

量子几何的非定域性

• 批准号: RGPIN-2016-04658
• 负责人: Freidel, Laurent
• 金额: $ 3.64万
• 依托单位: University of Waterloo
• 依托单位国家: 加拿大
• 项目类别: Discovery Grants Program - Individual
• 财政年份: 2016
• 资助国家: 加拿大
• 起止时间: 2016-01-01 至 2017-12-31
• 项目状态: 已结题
• 来源: https://www.nserc-crsng.gc.ca/ase-oro/Details-Detailles_eng.asp?id=615219
• 关键词: Non; locality; Quantum; geometry

Our understanding of modern physics and the physical universe rests on two cornerstones: quantum mechanics and general relativity. Unifying these two theories is a theoretical necessity in the sense that when combined, they predict their own demise. The search for a unified theory has been an extremely challenging and fruitful pursuit, and tremendous progress has been made in the past 20 years; however it still remains the outstanding fundamental question for theoretical physicists in the twenty-first century. The challenge is twofold: on the experimental side, there is a total absence of clear data, while on the theory side the opposite is true: We seem to have a plethora of possible candidates or approaches, such as string theory or AdS/CFT holography, which change the nature of the spacetime probes; or loop gravity, spin foam models causal sets or dynamical triangulations, which have a built-in discretisation of space; or non-commutative field theory, asymptotic safety or emergent gravity developed in the more conventional context of field theory. There is, however, a thread common in this diversity: these approaches all include at their foundation a form of non-locality; moreover recent results show that major progress is possible via a frontal attack on the question of non-locality itself. The goal of my research program is to focus on this common thread and propose a program to study the non-locality of quantum geometry from first principles. My past work work in quantum gravity has given me great expertise into the structure of quantum geometry. My recent work has proposed an underlying principle: relative locality, which sharpens the question of non-locality and gives us a framework to address it. I also have uncovered a realization of string theory called metastring, that incorporates relative locality in its foundation. Armed with these, my plan is to develop the study of quantum geometry, relative locality and the metastring into a framework that allows us to address directly the question of non-locality in quantum gravity. The goal is twofold: I intend to make specific progress on each subject, in particular by studying the consistency of the dynamics of quantum geometry, developing a better and deeper formulation of the principle of relative locality, and progressing towards a proof of the full consistency of the metastring. I also intend to provide a theoretical framework that will allow to study the question of non-Locality in its own right and give us with a common umbrella to understand all the different approaches. Another part of my research program is to advance the exciting idea that the dynamics of gravity could be formulated in terms of non equilibrium thermodynamics. I plan to develop this correspondence in the non-equilibrium context. Such a correspondence would open the way toward a constituent picture of gravity at the quantum level and give us clues on the quantum nature of geometry.

我们对现代物理学和物理宇宙的理解依赖于两个基石：量子力学和广义相对论。统一这两种理论是理论上的必要性，因为当它们结合起来时，它们就预示着自己的灭亡。寻找统一理论是一项极具挑战性且卓有成效的追求，在过去20年里取得了巨大进展；然而，对于二十一世纪的理论物理学家来说，它仍然是一个悬而未决的基本问题。 挑战是双重的：在实验方面，完全缺乏明确的数据，而在理论方面，情况恰恰相反：我们似乎有太多可能的候选者或方法，例如弦理论或 AdS/CFT 全息术，它们改变了时空探测器的性质；或循环重力、旋转泡沫模型因果集或动态三角测量，它们具有内置的空间离散化；或非交换场论、渐近安全性或在更传统的场论背景下发展起来的涌现引力。 然而，这种多样性中有一个共同点：这些方法都在其基础上包含了一种非局部性形式；此外，最近的结果表明，通过正面攻击非局域性问题本身，可以取得重大进展。我的研究计划的目标是关注这个共同点，并提出一个从第一原理研究量子几何非定域性的计划。 我过去在量子引力方面的工作使我在量子几何结构方面拥有丰富的专业知识。我最近的工作提出了一个基本原则：相对局部性，它加剧了非局部性问题，并为我们提供了解决该问题的框架。我还发现了一种称为元串的弦理论实现，它在其基础中融入了相对局部性。有了这些，我的计划是将量子几何、相对局域性和元串的研究发展成一个框架，使我们能够直接解决量子引力中的非局域性问题。我的目标是双重的：我打算在每个主题上取得具体进展，特别是通过研究量子几何动力学的一致性，开发相对局部性原理的更好、更深入的表述，并逐步证明元串的完全一致性。我还打算提供一个理论框架，使我们能够研究非地方性问题本身，并为我们提供一个共同的保护伞来理解所有不同的方法。 我的研究计划的另一部分是提出一个令人兴奋的想法，即重力动力学可以用非平衡热力学来表述。我计划在非平衡背景下发展这种对应关系。这样的对应关系将为我们在量子层面上绘制引力的组成图开辟道路，并为我们提供关于几何的量子本质的线索。