Topology and Quantum Theory in Interaction
Topology and Quantum Theory in
Interaction
复制标题
相互作用中的拓扑和量子理论
DOI：
10.1090/conm/718
复制
发表时间：
2018
期刊：
影响因子：
--
通讯作者：
Ryan E. Grady
中科院分区：
文献类型：
--
作者：
David Ayala;D. Freed;Ryan E. Grady
本卷包含了在QFT拓扑和几何方法的NSF-CBMS区域会议的会议记录，从7月31日至2017年8月4日，在蒙大拿州博兹曼的蒙大拿州立大学举行。近几十年来，有一种运动将量子场论公理化为数学结构。在另一个方向上，人们可以要求用物理学来检验这些公理系统。它们能被用来重新推导量子理论的已知事实吗？或者，更好的是，它们能成为解决开放问题的框架吗？最近，弗里德和霍普金斯提供了一个解决凝聚态理论中的分类问题的方法，该方法最终是基于格雷姆·西格尔的场论公理。论文包含在这卷放大各个方面的自由霍普金斯计划，发展一些范畴理论，这背后的协边假设，主要结构定理拓扑场论，并涉及到科斯特洛的方法微扰量子场论。关于后者的两篇论文使用这个框架来恢复一些物理理论的基本结果：二维西格玛模型和玻色弦。也许令人惊讶的是，这样稀疏的公理系统编码了足够的结构来证明物理学中的重要结果。这些成功可以被看作是一种鼓励，即公理系统至少在阐明量子场论是什么的正确轨道上。
This volume contains the proceedings of the NSF-CBMS Regional Conference on Topological and Geometric Methods in QFT, held from July 31–August 4, 2017, at Montana State University in Bozeman, Montana. In recent decades, there has been a movement to axiomatize quantum field theory into a mathematical structure. In a different direction, one can ask to test these axiom systems against physics. Can they be used to rederive known facts about quantum theories or, better yet, be the framework in which to solve open problems? Recently, Freed and Hopkins have provided a solution to a classification problem in condensed matter theory, which is ultimately based on the field theory axioms of Graeme Segal. Papers contained in this volume amplify various aspects of the Freed–Hopkins program, develop some category theory, which lies behind the cobordism hypothesis, the major structure theorem for topological field theories, and relate to Costello's approach to perturbative quantum field theory. Two papers on the latter use this framework to recover fundamental results about some physical theories: two-dimensional sigma-models and the bosonic string. Perhaps it is surprising that such sparse axiom systems encode enough structure to prove important results in physics. These successes can be taken as encouragement that the axiom systems are at least on the right track toward articulating what a quantum field theory is.