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 / by Marcel Bischoff, Yasuyuki Kawahigashi, Roberto Longo, Karl-Henning Rehren.

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, Karl-Henning (Author)
Corporate Author: SpringerLink (Online service)
Format: eBook
Language:English
Published: Cham : Springer International Publishing : Imprint: Springer, 2015.
Edition:1st ed. 2015.
Series:SpringerBriefs in Mathematical Physics, 3
Springer eBook Collection.
Subjects:
Quantum field theory.
String theory.
Mathematical physics.
Algebra.
Electronic resources (E-books)
Online Access:Click to view e-book
Holy Cross Note:Loaded electronically.
Electronic access restricted to members of the Holy Cross Community.
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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