Quantum Gravity and the Functional Renormalization Group: The Road towards Asymptotic Safety(Cambridge Monographs on Mathematical Physics)

During the past two decades the gravitational asymptotic safety scenario has undergone a major transition from an exotic possibility to a serious contender for a realistic theory of quantum gravity. It aims at a mathematically consistent quantum description of the gravitational interaction and the geometry of spacetime within the realm of quantum field theory, which keeps its predictive power at the highest energies. This volume provides a self-contained pedagogical introduction to asymptotic safety, and introduces the functional renormalization group techniques used in its investigation, along with the requisite computational techniques. The foundational chapters are followed by an accessible summary of the results obtained so far. It is the first detailed exposition of asymptotic safety, providing a unique introduction to quantum gravity and it assumes no previous familiarity with the renormalization group. It serves as an important resource for both practising researchers and graduate students entering this maturing field.

Table of Contents:
1. A quantum field theory of gravity; 2. The functional renormalization group; 3. The asymptotic safety mechanism; 4. A functional renormalization group for gravity; 5. Truncations of single-metric type; 6. Bi-metric truncations; 7. Conformally reduced gravity; 8. The reconstruction problem; 9. Alternative field variables; 10. Matter coupled to quantum gravity; 11. Towards phenomenology; 12. Miscellanea; Appendix A. Notation and conventions; Appendix B. Organizing the derivative expansion; Appendix C. Metric variations; Appendix D. Heat Kernel techniques; Appendix E. Cutoff- and threshold functions; Appendix F. Field decompositions; References; Index.

About the Author :
Martin Reuter is a Professor of Theoretical Physics at the Johannes Gutenberg Universität Mainz, Germany. He previously worked at the European Laboratory for Particle Physics, CERN, in Geneva, the DESY laboratory in Hamburg, and the Leibniz Universität Hannover. In the 1990s, he initiated the exploration of quantum gravity and the Asymptotic Safety scenario by means of the functional renormalization group and subsequently played a key role in developing the program into its present form. Frank Saueressig is Associate Professor at the Radboud Universiteit Nijmegen. Before his appointment, he held research positions at Utrecht University, the Institut de Physique Théorique at CEA/Saclay, and an Emmy Noether fellowship at the Johannes Gutenberg University Mainz. With more than seventy scientific publications in the field of quantum gravity he is among the leading young talents in the field.

Review :
'This book summarizes the developments in a specific approach to quantum gravity, called the 'asymptotic safety' scenario, over the last thirty years. It provides a pedagogical account of the basic conceptual idea and methods of the approach, and should be a valuable resource for researchers in this field.' Ivan G. Avramidi, Mathematical Reviews Clippings