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 /

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 notion...

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Bibliographic Details
Main Authors: Bischoff, Marcel (Author), Kawahigashi, Yasuyuki (Author), Longo, Roberto (Author), Rehren, K.-H. (Karl-Henning) (Author)
Format: Electronic eBook
Language:English
Published: Cham : Springer International Publishing : Imprint: Springer, 2015.
Series:SpringerBriefs in mathematical physics ; 3.
Subjects:
Physics.
Algebra.
Mathematical physics.
Quantum field theory.
String models.
Quantum Field Theories, String Theory.
Mathematical Physics.
Online Access:Connect to this title online
Table of Contents:
  • 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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