Tensor Categories and Endomorphisms of von Neumann Algebras

with Applications to Quantum Field Theory

  • Marcel Bischoff
  • Yasuyuki Kawahigashi
  • Roberto Longo
  • Karl-Henning Rehren

Part of the SpringerBriefs in Mathematical Physics book series (BRIEFSMAPHY, volume 3)

Table of contents

  1. Front Matter
    Pages i-x
  2. Marcel Bischoff, Yasuyuki Kawahigashi, Roberto Longo, Karl-Henning Rehren
    Pages 1-4
  3. Marcel Bischoff, Yasuyuki Kawahigashi, Roberto Longo, Karl-Henning Rehren
    Pages 5-13
  4. Marcel Bischoff, Yasuyuki Kawahigashi, Roberto Longo, Karl-Henning Rehren
    Pages 15-40
  5. Marcel Bischoff, Yasuyuki Kawahigashi, Roberto Longo, Karl-Henning Rehren
    Pages 41-76
  6. Marcel Bischoff, Yasuyuki Kawahigashi, Roberto Longo, Karl-Henning Rehren
    Pages 77-91
  7. Marcel Bischoff, Yasuyuki Kawahigashi, Roberto Longo, Karl-Henning Rehren
    Pages 93-94

About this book

Introduction

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).

Keywords

Alpha-induction Conformal Field Theory Frobenius Algebras Morita Equivalence Q-systems Relativistic local QFT Representation Theory Topological QFT von Neumann Algebras

Authors and affiliations

  • Marcel Bischoff
    • 1
  • Yasuyuki Kawahigashi
    • 2
  • Roberto Longo
    • 3
  • Karl-Henning Rehren
    • 4
  1. 1.Universität GöttingenInstitut für Theoretische PhysikGöttingenGermany
  2. 2.Department of Mathematical Sciences and Kavli IPMU (WPI)The University of TokyoTokyoJapan
  3. 3.Dipartimento di MatematicaUniversità di Roma "Tor Vergata"RomeItaly
  4. 4.Universität GöttingenInstitut für Theoretische PhysikGöttingenGermany

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-319-14301-9
  • Copyright Information The Author(s) 2015
  • Publisher Name Springer, Cham
  • eBook Packages Physics and Astronomy
  • Print ISBN 978-3-319-14300-2
  • Online ISBN 978-3-319-14301-9
  • Series Print ISSN 2197-1757
  • Series Online ISSN 2197-1765
  • About this book