Tensorial Methods and Renormalization in Group Field Theories

Nonfiction, Science & Nature, Science, Physics, Gravity, Nuclear Physics
Cover of the book Tensorial Methods and Renormalization in Group Field Theories by Sylvain Carrozza, Springer International Publishing
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Author: Sylvain Carrozza ISBN: 9783319058672
Publisher: Springer International Publishing Publication: April 12, 2014
Imprint: Springer Language: English
Author: Sylvain Carrozza
ISBN: 9783319058672
Publisher: Springer International Publishing
Publication: April 12, 2014
Imprint: Springer
Language: English

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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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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