This book, first published in 2007, is an introductory textbook on quantum field theory in gravitational backgrounds intended for undergraduate and beginning graduate students in the fields of theoretical astrophysics, cosmology, particle physics, and string theory. The book covers the basic (but essential) material of quantization of fields in an expanding universe and quantum fluctuations in inflationary spacetime. It also contains a detailed explanation of the Casimir, Unruh, and Hawking effects, and introduces the method of effective action used for calculating the back-reaction of quantum systems on a classical external gravitational field. The broad scope of the material covered will provide the reader with a thorough perspective of the subject. Every major result is derived from first principles and thoroughly explained. The book is self-contained and assumes only a basic knowledge of general relativity. Exercises with detailed solutions are provided throughout the book.

Review

"... A groundbreaker in being an introductory text on quantum field theory in gravitational backgrounds, intended for undergraduate and beginning graduate students."

Lewis H. Ryder, Mathematical Reviews

"The treatment is clear throughout and the mathematical manipulations straightforward. This book is to be greatly recommended to anyone with an interest in contemporary theoretical cosmology; it is a most valuable contribution to the literature on the early universe."

Contemporary Physics

Book Description

This book, first published in 2007, cover quantum field theory for undergraduates and graduates in theoretical astrophysics, cosmology, particle physics, and string theory.

Table of Contents

Part I. Canonical Quantization and Particle Production

1. Overview: A Taste of Quantum Fields

2. Reminder: Classical and Quantum Theory

3. Driven Harmonic Oscillator

4. From Harmonic Oscillators to Fields

5. Reminder: Classical Fields

6. Quantum Fields in Expanding Universe

7. Quantum Fields in the de Sitter Universe

8. Unruh Effect

9. Hawking Effect. Thermodynamics of Black Holes

10. The Casimir Effect

Part II. Path Integrals and Vacuum Polarization

11. Path Integrals

12. Effective Action

13. Calculation of Heat Kernel

14. Results from Effective Action

Appendix 1. Mathematical Supplement

Appendix 2. Backreaction Derived from Effective Action

Appendix 3. Mode Expansions Cheat Sheet

Appendix 4. Solutions to Exercises

About the Authors

Viatcheslav Mukhanov is Professor of Physics at Ludwig-Maximilians-University, Munich. His main result is the theory of inflationary cosmological perturbations. Professor Mukhanov is author of Physical Foundations of Cosmology (Cambridge University Press, 2005). He also serves on the editorial boards of leading research journals and is Scientific Director of the Journal of Cosmology and Astroparticle Physics (JCAP).

Sergei Winitzki  is Research Associate in the Department of Physics at Ludwig-Maximilians-University, Munich. His main areas of research include quantum cosmology, the theory of dark energy, the global structure of spacetime, and quantum gravity.