量子场论与引力中的驯顺性与复杂性
Tameness and Complexity in Quantum Field Theory and Gravity
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中文总结 AI 辅助
本文利用驯顺几何与尖锐o-极小性理论，系统证明量子场论与引力中多类物理函数和理论具有驯顺性，并论证其与量子引力有限性一致，支持有效理论具有有限复杂性。
中文摘要 AI 辅助
有限性似乎在物理学定律背后的数学结构中扮演着基础性角色。驯顺几何（tame geometry），由o-极小性理论定义，为精确化这一思想提供了框架。在本论文中，我们研究了量子场论与量子引力应用中驯顺性与复杂性有限性的概念，并证明了多类物理函数和理论是驯顺的。为了量化这些思想，我们使用新颖的尖锐o-极小性理论来度量物理对象的复杂性。分析涵盖了量子力学中的波函数、经典场构型、零维量子场论中的非微扰可观测量、宇宙学关联函数以及有效场论的拉格朗日量。最后，我们论证物理学中驯顺性的出现与量子引力中有限性的表现相一致，共同趋向于这样一个观点：量子引力的有效理论允许具有有限复杂性的描述。本论文包含一篇导论性综述，供希望熟悉驯顺几何及其在物理学中应用的读者阅读。
英文摘要
Finiteness appears to play a fundamental role in the mathematical structures underlying the laws of physics. Tame geometry, defined by the theory of o-minimality, provides a framework for making this idea precise. In this thesis we study the concept of tameness and finiteness of complexity across applications in quantum field theory and quantum gravity, and demonstrate that many classes of physical functions and theories are tame. To quantify these ideas, we use the novel theory of sharp o-minimality to measure the complexity of physical objects. The analysis covers wavefunctions in quantum mechanics, classical field configurations, non-perturbative observables in zero-dimensional quantum field theories, cosmological correlation functions, and Lagrangians of effective field theories. Finally, we argue that the emergence of tameness in physics aligns with manifestations of finiteness in quantum gravity, converging towards the idea that effective theories of quantum gravity admit a description of finite complexity. The thesis contains an introductory review for readers who wish to get familiar with tame geometry and its applications to physics.
发表机构
- Utrecht University（乌得勒支大学）
机构由 AI 辅助整理，请以论文原文为准。
