Springer Theses

Tensorial Methods and Renormalization in Group Field Theories

Authors: Carrozza, Sylvain

  • Nominated as an outstanding Ph.D. thesis by Université Paris-Sud at Orsay, France
  • Provides pedagogical reviews of both colored and tensorial group field theories
  • Gives a detailed introduction in the first three chapters to the concepts and assumptions entering the technical discussions of the later chapters
  • Gathers recent results on the asymptotics and renormalization of group field theories in full technical detail, material not available in any other book or review (the original articles being scattered over several journals)
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  • ISBN 978-3-319-05867-2
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Hardcover $129.00
price for USA
  • ISBN 978-3-319-05866-5
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Softcover $129.00
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  • Due: October 20, 2016
  • ISBN 978-3-319-35887-1
  • Free shipping for individuals worldwide
Rent the ebook  
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About this book

The main focus of this thesis is the mathematical structure of Group Field Theories (GFTs) from the point of view of renormalization theory. Such quantum field theories are found in approaches to quantum gravity related, on the one hand, to Loop Quantum Gravity (LQG) and on the other, to matrix- and tensor models. Background material on these topics, including conceptual and technical aspects, are introduced in the first chapters. The work then goes on to explain how the standard tools of Quantum Field Theory can be generalized to GFTs and exploited to study the large cut-off behaviour and renormalization group transformations of the latter. Among the new results derived in this context are a proof of renormalizability of a three-dimensional GFT with gauge group SU(2), which opens the way to applications of the formalism to quantum gravity.

About the authors

Sylvain Carrozza studied physics and mathematics at the École Normale Supérieure de Lyon. He then completed his doctoral studies in theoretical physics, with joint affiliation at the University of Paris-Sud and at the Max Planck Institute for Gravitational Physics. He is currently a postdoctoral researcher at the University of Aix-Marseille.

Table of contents (8 chapters)

  • Introduction and Motivation

    Carrozza, Sylvain

    Pages 1-15

  • Two Paths to Group Field Theories

    Carrozza, Sylvain

    Pages 17-47

  • Colors and Tensor Invariance

    Carrozza, Sylvain

    Pages 49-60

  • Large N Expansion in Topological Group Field Theories

    Carrozza, Sylvain

    Pages 61-109

  • Renormalization of Tensorial Group Field Theories: Generalities

    Carrozza, Sylvain

    Pages 111-150

Buy this book

eBook $99.00
price for USA (gross)
  • ISBN 978-3-319-05867-2
  • Digitally watermarked, DRM-free
  • Included format: PDF, EPUB
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $129.00
price for USA
  • ISBN 978-3-319-05866-5
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Softcover $129.00
price for USA
  • Customers within the U.S. and Canada please contact Customer Service at 1-800-777-4643, Latin America please contact us at +1-212-460-1500 (Weekdays 8:30am – 5:30pm ET) to place your order.
  • Due: October 20, 2016
  • ISBN 978-3-319-35887-1
  • Free shipping for individuals worldwide
Rent the ebook  
  • Rental duration: 1 or 6 month
  • low-cost access
  • online reader with highlighting and note-making option
  • can be used across all devices
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Bibliographic Information

Bibliographic Information
Book Title
Tensorial Methods and Renormalization in Group Field Theories
Authors
Series Title
Springer Theses
Copyright
2014
Publisher
Springer International Publishing
Copyright Holder
Springer International Publishing Switzerland
eBook ISBN
978-3-319-05867-2
DOI
10.1007/978-3-319-05867-2
Hardcover ISBN
978-3-319-05866-5
Softcover ISBN
978-3-319-35887-1
Series ISSN
2190-5053
Edition Number
1
Number of Pages
XV, 226
Number of Illustrations and Tables
51 b/w illustrations
Topics