Tensorial Methods And Renormalization In Group Field Theories

Download or read book Tensorial Methods and Renormalization in Group Field Theories written by Sylvain Carrozza and published by Springer Science & Business Media. This book was released on 2014-04-12 with total page 236 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.