Quantum Gravity and the Functional Renormalization Group
The Road towards Asymptotic Safety

A self-contained pedagogical introduction to asymptotic safety and the functional renormalization group in quantum gravity, for graduate students and researchers.

Martin Reuter (Author), Frank Saueressig (Author)

9781107107328, Cambridge University Press

Hardback, published 3 January 2019

354 pages
25.5 x 18 x 2.4 cm, 0.78 kg

'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

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.

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.

Subject Areas: Mathematical physics [PHU], Relativity physics [PHR], Quantum physics [quantum mechanics & quantum field theory PHQ]