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).| ISBN: | 9783319143002 |
| Publication date: | 23rd January 2015 |
| Author: | Marcel Bischoff, Yasuyuki Kawahigashi, Roberto Longo, KarlHenning Rehren |
| Publisher: | Springer an imprint of Springer International Publishing |
| Format: | Paperback |
| Pagination: | 94 pages |
| Series: | SpringerBriefs in Mathematical Physics |
| Genres: |
Particle and high-energy physics Mathematical physics Algebra |