Tensorial Methods and Renormalization in Group Field Theories

Softcover Nachdruck of the original 1. Auflage 2014
ISBN: 978-3-319-35887-1
Verlag: Springer International Publishing

Buch, Englisch, 226 Seiten, Previously published in hardcover, Format (B × H): 155 mm x 235 mm, Gewicht: 3752 g

Reihe: Springer Theses

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.

Zielgruppe

Research

Autoren/Hrsg.

Carrozza, Sylvain

Fachgebiete

• Naturwissenschaften Physik Physik Allgemein Theoretische Physik, Mathematische Physik, Computerphysik
• Naturwissenschaften Physik Quantenphysik

Inhaltsverzeichnis

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.

Über Autor(innen)

Sylvain Carrozza studied physics and mathematics at the École Normale Supérieure de Lyon. He then completed his doctoral studies in theoretical physics, with joint affiliation at the University of Paris-Sud and at the Max Planck Institute for Gravitational Physics. He is currently a postdoctoral researcher at the University of Aix-Marseille.