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.
| ISBN: | 9783319358871 |
| Publication date: | 3rd September 2016 |
| Author: | Sylvain Carrozza |
| Publisher: | Springer an imprint of Springer International Publishing |
| Format: | Paperback |
| Pagination: | 226 pages |
| Series: | Springer Theses |
| Genres: |
Particle and high-energy physics Gravity Mathematical physics Groups and group theory Cosmology and the universe |
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.
Tensorial Methods and Renormalization in Group Field Theories features in the following genres: Particle and high-energy physics, Gravity, Mathematical physics, Groups and group theory, Cosmology and the universe
Tensorial Methods and Renormalization in Group Field Theories is available in Paperback, Hardback
Tensorial Methods and Renormalization in Group Field Theories was written by Sylvain Carrozza and published by Springer an imprint of Springer International Publishing
Tensorial Methods and Renormalization in Group Field Theories has 226 pages
Yes it is part of Springer Theses series