Semiclassical and Stochastic Gravity
Quantum Field Effects on Curved Spacetime

An overview of semi-classical gravity theory and stochastic gravity as theories of quantum gravity in curved space-time.

Bei-Lok B. Hu (Author), Enric Verdaguer (Author)

9780521193573, Cambridge University Press

Hardback, published 5 March 2020

614 pages, 10 b/w illus.
25.4 x 18.3 x 3.7 cm, 1.21 kg

'The aim is to help the reader get familiarized with the new topics and techniques through working out some concrete representative problems. The result is a compulsive text quite useful for graduate students and newcomers.' Farhang Loran, zbMATH

The two pillars of modern physics are general relativity and quantum field theory, the former describes the large scale structure and dynamics of space-time, the latter, the microscopic constituents of matter. Combining the two yields quantum field theory in curved space-time, which is needed to understand quantum field processes in the early universe and black holes, such as the well-known Hawking effect. This book examines the effects of quantum field processes back-reacting on the background space-time which become important near the Planck time (10-43 sec). It explores the self-consistent description of both space-time and matter via the semiclassical Einstein equation of semiclassical gravity theory, exemplified by the inflationary cosmology, and fluctuations of quantum fields which underpin stochastic gravity, necessary for the description of metric fluctuations (space-time foams). Covering over four decades of thematic development, this book is a valuable resource for researchers interested in quantum field theory, gravitation and cosmology.

Preface
1. Overview: main themes. Key issues. Reader's guide
Part I. Effective Action and Regularization, Stress Tensor and Fluctuations: 2. `In-out' effective action. Dimensional regularization
3. `In-in' effective action. Stress tensor. Thermal fields
4. Stress-energy tensor and correlators: zeta-function method
5. Stress-energy tensor and correlation. Point separation
Part II. Infrared Behavior, 2Pi, 1/n Backreaction and Semiclassical Gravity: 6. Infrared behavior of interacting quantum fields
7. Advanced field theory topics
8. Backreaction of early universe quantum processes
Part III. Stochastic Gravity: 9. Metric correlations at one-loop: in-in and large N
10. The Einstein-Langevin equation
11. Metric fluctuations in Minkowski spacetime
Part IV. Cosmological and Black Hole Backreaction with Fluctuations: 12. Cosmological backreaction with fluctuations
13. Structure formation in the early universe
14. Black hole backreaction and fluctuations
Part V. Quantum Curvature Fluctuations in De Sitter Spacetime: 15. Stress-energy tensor fluctuations in de Sitter space
16. Two-point metric perturbations in de Sitter
17. Riemann tensor correlator in de Sitter
18. Epilogue: linkage with quantum gravity
References
Index.

Subject Areas: Mathematical physics [PHU], Relativity physics [PHR], Gravity [PHDV], Cosmology & the universe [PGK]