Tensorial Methods and Renormalization in Group Field Theories by Sylvain CarrozzaTensorial Methods and Renormalization in Group Field Theories by Sylvain Carrozza

Tensorial Methods and Renormalization in Group Field Theories

bySylvain Carrozza

Hardcover | April 25, 2014

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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.
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-Mars...
Title:Tensorial Methods and Renormalization in Group Field TheoriesFormat:HardcoverDimensions:226 pagesPublished:April 25, 2014Publisher:Springer-Verlag/Sci-Tech/TradeLanguage:English

The following ISBNs are associated with this title:

ISBN - 10:3319058665

ISBN - 13:9783319058665

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Table of Contents

Motivations and Scope of the Present Work.- Two Paths to Group Field Theories.- Colors and Tensor Invariance.- Large N Expansion in Topological Group Field Theories.- Renormalization of Tensorial Group Field Theories: Generalities.- Super-Renormalizable U(1) Models in Four Dimensions.- Just-Renormalizable SU(2) Model in Three Dimensions.