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SpringerBriefs in Mathematical Physics

Tensor Categories and Endomorphisms of von Neumann Algebras

with Applications to Quantum Field Theory

Authors: Bischoff, M., Kawahigashi, Y., Longo, R., Rehren, K.-H.

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  • ISBN 978-3-319-14301-9
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Softcover $69.99
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About this book

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).

Reviews

“The volume gives a coherent overview of some recent mathematical developments in the study of endomorphisms of von Neumann algebras and their applications in algebraic quantum field theory. … every chapter has its own list of references, which points the reader to more detailed literature. … Anyone who wishes to understand the recent advances in our understanding of endomorphisms of von Neumann algebras … should find this book a valuable resource.” (Ko Sanders, Mathematical Reviews, January, 2016)


Table of contents (6 chapters)

  • Introduction

    Bischoff, Marcel (et al.)

    Pages 1-4

  • Homomorphisms of von Neumann Algebras

    Bischoff, Marcel (et al.)

    Pages 5-13

  • Frobenius Algebras, Q-Systems and Modules

    Bischoff, Marcel (et al.)

    Pages 15-40

  • Q-System Calculus

    Bischoff, Marcel (et al.)

    Pages 41-76

  • Applications in QFT

    Bischoff, Marcel (et al.)

    Pages 77-91

Buy this book

eBook $54.99
price for USA in USD (gross)
  • ISBN 978-3-319-14301-9
  • Digitally watermarked, DRM-free
  • Included format: PDF, EPUB
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Softcover $69.99
price for USA in USD
  • ISBN 978-3-319-14300-2
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
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Bibliographic Information

Bibliographic Information
Book Title
Tensor Categories and Endomorphisms of von Neumann Algebras
Book Subtitle
with Applications to Quantum Field Theory
Authors
Series Title
SpringerBriefs in Mathematical Physics
Series Volume
3
Copyright
2015
Publisher
Springer International Publishing
Copyright Holder
The Author(s)
eBook ISBN
978-3-319-14301-9
DOI
10.1007/978-3-319-14301-9
Softcover ISBN
978-3-319-14300-2
Series ISSN
2197-1757
Edition Number
1
Number of Pages
X, 94
Number of Illustrations
138 b/w illustrations
Topics