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  • Book
  • © 2014

Tensorial Methods and Renormalization in Group Field Theories

Authors:

  1. Sylvain Carrozza

    1. Laboratoire de Physique Théorique d'Orsay, Université Paris-Sud, Orsay, France

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  • 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)
  • Includes supplementary material: sn.pub/extras

Part of the book series: Springer Theses (Springer Theses)

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Table of contents (8 chapters)

  1. Front Matter

    Pages i-xv
    PDF

  2. Introduction and Motivation

    • Sylvain Carrozza
    Pages 1-15

  3. Two Paths to Group Field Theories

    • Sylvain Carrozza
    Pages 17-47

  4. Colors and Tensor Invariance

    • Sylvain Carrozza
    Pages 49-60

  9. Conclusions and Perspectives

    • Sylvain Carrozza
    Pages 213-220

  10. Back Matter

    Pages 221-226
    PDF
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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.
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Keywords

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Authors and Affiliations

  • Laboratoire de Physique Théorique d'Orsay, Université Paris-Sud, Orsay, France

    Sylvain Carrozza

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About the author

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.
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Buy it now

eBook USD 84.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Hardcover Book USD 109.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Other ways to access

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