Tensor Categories and Endomorphisms of von Neumann Algebras with Applications to Quantum Field Theory /

• Κύριοι συγγραφείς: Bischoff, Marcel (Συγγραφέας), Kawahigashi, Yasuyuki (Συγγραφέας), Longo, Roberto (Συγγραφέας), Rehren, Karl-Henning (Συγγραφέας)
• Συγγραφή απο Οργανισμό/Αρχή: SpringerLink (Online service)
• Μορφή: Ηλεκτρονική πηγή Ηλ. βιβλίο
• Γλώσσα: English
• Έκδοση: Cham : Springer International Publishing : Imprint: Springer, 2015.
• Σειρά: SpringerBriefs in Mathematical Physics, 3
• Θέματα: Physics.; Algebra.; Mathematical physics.; Quantum field theory.; String theory.; Quantum Field Theories, String Theory.; Mathematical Physics.

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...

Πίνακας περιεχομένων:

• 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.