Tensorial Methods and Renormalization in Group Field Theories

• Main Author: Carrozza, Sylvain (Author)
• Corporate Author: SpringerLink (Online service)
• Format: Electronic eBook
• Language: English
• Published: Cham : Springer International Publishing : Imprint: Springer, 2014.
• Series: Springer Theses, Recognizing Outstanding Ph.D. Research,
• Subjects: Physics.; Group theory.; Mathematical physics.; Gravitation.; Cosmology.; Elementary particles (Physics).; Quantum field theory.; Elementary Particles, Quantum Field Theory.; Classical and Quantum Gravitation, Relativity Theory.; Group Theory and Generalizations.; Mathematical Physics.

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- an...

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.