Tensor categories and endomorphisms of Von Neumann algebras with applications to quantum field theory / [electronic resource] :

• 其他作者：
  • Bischoff, Marcel.
  • SpringerLink (Online service)
• 其他題名：
  • SpringerBriefs in mathematical physics,
• 出版： Cham : Springer International Publishing :Imprint: Springer
• 叢書名： SpringerBriefs in mathematical physics,v.3
• 主題： Calculus of tensors , Von Neumann algebras. , Quantum field theory , Physics , Quantum Field Theories, String Theory. , Mathematical physics , Algebra
• ISBN： 9783319143019 (electronic bk.) 、 9783319143002 (paper)
• FIND@SFXID: CGU
• 資料類型: 電子書
• 內容註: Introduction -- Homomorphisms of von Neumann algebras -- Endomorphisms of infinite factors -- Homomorphisms and subfactors -- Non-factorial extensions -- Frobenius algebras, Q-systems and modules -- C* Frobenius algebras -- Q-systems and extensions -- The canonical Q-system -- Modules of Q-systems -- Induced Q-systems and Morita equivalence -- Bimodules -- Tensor product of bimodules -- Q-system calculus -- Reduced Q-systems -- Central decomposition of Q-systems -- Irreducible decomposition of Q-systems -- Intermediate Q-systems -- Q-systems in braided tensor categories -- a-induction -- Mirror Q-systems -- Centre of Q-systems -- Braided product of Q-systems -- The full centre -- Modular tensor categories -- The braided product of two full centres -- Applications in QFT -- Basics of algebraic quantum field theory -- Hard boundaries -- Transparent boundaries -- Further directions -- Conclusions.
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• 摘要註: 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).
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