© 2014

Tensorial Methods and Renormalization in Group Field Theories


Part of the Springer Theses book series (Springer Theses)

Table of contents

  1. Front Matter
    Pages i-xv
  2. Sylvain Carrozza
    Pages 1-15
  3. Sylvain Carrozza
    Pages 17-47
  4. Sylvain Carrozza
    Pages 49-60
  5. Sylvain Carrozza
    Pages 213-220
  6. Back Matter
    Pages 221-226

About this book


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.


Colored GFT Group Field Theory Large Cutoff Behavior Lattice Gauge Theory Loop Quantum Gravity Quantum Gravity Renormalization Group Transformations Spin Foam Tensorial GFT

Authors and affiliations

  1. 1.Laboratoire de Physique Théorique d'OrsayUniversité Paris-SudOrsayFrance

About the authors

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.

Bibliographic information