## Quantum Field Theory in Curved Spacetime: Quantized Fields and GravityQuantum field theory in curved spacetime has been remarkably fruitful. It can be used to explain how the large-scale structure of the universe and the anisotropies of the cosmic background radiation that we observe today first arose. Similarly, it provides a deep connection between general relativity, thermodynamics, and quantum field theory. This book develops quantum field theory in curved spacetime in a pedagogical style, suitable for graduate students. The authors present detailed, physically motivated, derivations of cosmological and black hole processes in which curved spacetime plays a key role. They explain how such processes in the rapidly expanding early universe leave observable consequences today, and how in the context of evaporating black holes, these processes uncover deep connections between gravitation and elementary particles. The authors also lucidly describe many other aspects of free and interacting quantized fields in curved spacetime. |

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### Contents

1 | |

2 Basics of quantum fields in curved spacetimes | 36 |

3 Expectation values quadratic in fields | 93 |

4 Particle creation by black holes | 152 |

5 The oneloop effective action | 184 |

Nongauge theories | 268 |

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### Common terms and phrases

adiabatic order algebra amplitude anticommutation arbitrary asymptotic black hole boundary conditions calculation canonical commutation relations Chapter classical action coefficients condensed notation conformally invariant consider constant cosmological cosmological constant counterterms covariant derivative curvature curved spacetime deﬁned deﬁnition denotes density DeWitt dimensional regularization Dirac Dirac equation Dirac spinor discussed divergences effective potential energy-momentum tensor energy—momentum tensor evaluated event horizon expectation value expression factor Feynman ﬁeld equation field space ﬁnd ﬁnite ﬁrst follows functional integral gauge conditions gauge theories gauge transformation given gravitational Green function inﬁnitesimal inﬁnity inﬂation kernel Lagrangian Lorentz Lorentz transformation massless matrix metric Minkowski spacetime momentum normal coordinates null geodesics obtain operator parameter Parker particles perturbations Phys physical quantized quantum ﬁeld theory renormalization representation result Riemann normal coordinates right—hand side satisﬁes satisfy scalar ﬁeld Schwarzschild Section Sitter solution spacetime dimension spatial spectrum spinor symmetry theory in curved trace anomaly vacuum vanishes vector