Tensor Categories and Endomorphisms of von Neumann Algebras: with Applications to Quantum Field Theory
Tensor Categories and Endomorphisms of von Neumann Algebras: with Applications to Quantum Field Theory
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DOI：
10.1007/978-3-319-14301-9
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发表时间：
2014-07
期刊：
影响因子：
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通讯作者：
M. Bischoff;R. Longo;Yasuyuki Kawahigashi;K. Rehren
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文献类型：
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作者：
M. Bischoff;R. Longo;Yasuyuki Kawahigashi;K. Rehren
C* 张量类别是算子代数和量子场论的交汇点。它们是（适当无限的）冯·诺依曼代数同态和量子可观测量表示的基本统一概念。本介绍性文本回顾了基本概念及其在不同背景下的交叉关系。重点是作为完整不变量的 Q 系统，无论是子因子还是量子场论模型的扩展。它对 Q 系统进行各种操作（多次分解、镜像 Q 系统、编织产品、Q 系统的中心和全中心），其中一些操作仅在存在编织时定义。最后一章简要阐述了正文中提出的数学结构与量子场论（特别是二维共形场论，也有边界或缺陷）应用的相关性。
C* tensor categories are a point of contact where Operator Algebras and Quantum Field Theory meet. They are the underlying unifying concept for homomorphisms of (properly infinite) von Neumann algebras and representations of quantum observables. The present introductory text reviews the basic notions and their cross-relations in different contexts. The focus is on Q-systems that serve as complete invariants, both for subfactors and for extensions of quantum field theory models. It proceeds with various operations on Q-systems (several decompositions, the mirror Q-system, braided product, centre and full centre of Q-systems) some of which are defined only in the presence of a braiding. The last chapter gives a brief exposition of the relevance of the mathematical structures presented in the main body for applications in Quantum Field Theory (in particular two-dimensional Conformal Field Theory, also with boundaries or defects).