Tensor Categories and Endomorphisms of von Neumann Algebras

with Applications to Quantum Field Theory

Nonfiction, Science & Nature, Science, Physics, Mathematical Physics, Quantum Theory
Cover of the book Tensor Categories and Endomorphisms of von Neumann Algebras by Marcel Bischoff, Yasuyuki Kawahigashi, Roberto Longo, Karl-Henning Rehren, Springer International Publishing
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Author: Marcel Bischoff, Yasuyuki Kawahigashi, Roberto Longo, Karl-Henning Rehren ISBN: 9783319143019
Publisher: Springer International Publishing Publication: January 13, 2015
Imprint: Springer Language: English
Author: Marcel Bischoff, Yasuyuki Kawahigashi, Roberto Longo, Karl-Henning Rehren
ISBN: 9783319143019
Publisher: Springer International Publishing
Publication: January 13, 2015
Imprint: Springer
Language: English

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).

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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).

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