## Introduction to Quantum Effects in GravityThis 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. |

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### Contents

classical and quantum theory | 13 |

Driven harmonic oscillator | 33 |

From harmonic oscillators to fields | 42 |

classical fields | 54 |

Quantum fields in expanding universe | 64 |

Quantum fields in the de Sitter universe | 85 |

Unruh effect | 97 |

Hawking effect Thermodynamics of black holes | 109 |

Path integrals | 131 |

Effective action | 146 |

Calculation of heat kernel | 170 |

Results from effective action | 180 |

Mathematical supplement | 193 |

Backreaction derived from effective action | 212 |

Solutions to exercises | 218 |

272 | |

### Other editions - View all

Introduction to Quantum Effects in Gravity Viatcheslav Mukhanov,Sergei Winitzki Limited preview - 2007 |

### Common terms and phrases

accelerated observer amplitude analytic continuation arbitrary backreaction black hole boundary conditions calculations commutation relations complex compute conformal consider constant contour converges corresponding covariant curvature defined degrees of freedom described determine distribution divergent dºx effective action eigenvalues eigenvectors energy density energy-momentum tensor equation of motion Euclidean Exercise expectation value expression factor finite follows formula function f(x functional derivative gravitational field Green’s function Hamiltonian harmonic oscillator Hawking radiation heat kernel hence Hermitian Hilbert space horizon inertial infinite invariant Lagrangian linear Lorentzian matrix element metric Minkowski spacetime mode expansion mode functions momentum normalization obtain path integral physical propagator quantization quantum field theory quantum fluctuations quantum theory relativistic renormalization result rewrite Rindler satisfy scalar field Schrödinger equation Schwarzschild Sitter ſº solution spectrum Substituting time-independent Unruh effect vacuum energy vacuum fluctuations variable vector wave function well-defined