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Tensorial Methods and Renormalization in Group Field Theories
Author
Title
Tensorial Methods and Renormalization in Group Field Theories [electronic resource] / by Sylvain Carrozza.
ISBN
9783319058672
Publication
Cham : Springer International Publishing : Imprint: Springer, 2014.
Physical Description
XV, 226 p. 51 illus : online resource.
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Summary
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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Springer ebooks.
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Format
Books / Online
Language
English
Added to Catalog
May 07, 2014
Series
Springer Theses, Recognizing Outstanding Ph.D. Research,
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.
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