本书系统地介绍了引力中的量子场论方法，适合用作理论天体物理，宇宙学，粒子物理和超弦理论等专业的本科生和研究生教材。本书首先介绍了量子场论中的一般概念，重点讲解了利用量子场论方法研究引力，同时还介绍了基本且必要的不断扩张宇宙中的场量子化和膨胀时空中的量子涨落。此外，本书还详细讨论了Casimir效应，Unruh效应和霍金效应，并介绍了计算外部重力场中量子系统的反向反应的有效作用量。作者从最初的基本原理出发，经过演绎得出最终结果，并对最终结果做详细的解释，帮助读者对该领域建立完整的物理图像。本书内容全面，讲解深刻，附有习题及其答案。

Part I Canonical quantization and particle production

　1 Overview: a taste of quantum fields

1.1 Classical field

　　1.2 Quantum field and its vacuum state

　　1.3 The vacuum energy

　　1.4 Quantum vacuum fluctuations

　　1.5 Particle interpretation of quantum fields

　　1.6 Quantum field theory in classical backgrounds

　　1.7 Examples of particle creation

　2 Reminder: classical and quantum theory

　　2.1 Lagrangian formalism

　　2.1.1 Functional derivatives

　　2.2 Hamiltonian formalism

　　2.3 Quantization of Hamiltonian systems

　　2.4 Hilbert spaces and Dirac notation

　　2.5 Operators, eigenvalue problem and basis in a Hilbert space

　　2.6 Generalized eigenvectors and basic matrix elements

　　2.7 Evolution in quantum theory

　3 Driven harmonic oscillator

　　3.1 Quantizing an oscillator

　　3.2 The "in" and "out" states

　　3.3 Matrix elements and Green's functions

　4 From harmonic oscillators to fields

　　4.1 Quantum harmonic oscillators

　　4.2 From oscillators to fields

　　4.3 Quantizing fields in a flat spacetime

　　4.4 The mode expansion

　　4.5 Vacuum energy and vacuum fluctuations

　　4.6 The Schr'odinger equation for a quantum field

　5 Reminder: classical fields

　　5.1 The action functional

　　5.2 Real scalar field and its coupling to the gravity

　　5.3 Gauge invariance and coupling to the electromagnetic field

　　5.4 Action for the gravitational and gauge fields

　　5.5 Energy-momentum tensor

　6 Quantum fields in expanding universe

　　6.1 Classical scalar field in expanding background

　　6.1.1 Mode expansion

　　6.2 Quantization

　　6.3 Bogolyubov transformations

　　6.4 Hilbert space; "a- and b-particles"

　　6.5 Choice of the physical vacuum

　　6.5.1 The instantaneous lowest-energy state

　　6.5.2 Ambiguity of the vacuum state

　　6.6 Amplitude of quantum fluctuations

　　6.6.1 Comparing fluctuations in the vacuum and excited states

　　6.7 An example of particle production

　7 Quantum fields in the de Sitter universe

　　7.1 De Sitter universe

　　7.2 Quantization

　　7.2.1 Bunch-Davies vacuum

　　7.3 Fluctuations in inflationary universe

　8 Unruh effect

　　8.1 Accelerated motion

　　8.2 Comoving frame of accelerated observer

　　8.3 Quantum fields in inertial and accelerated frames

　　8.4 Bogolyubov transformations

　　8.5 Occupation numbers and Unmh temperature

　9 Hawking effect. Thermodynamics of black holes

　　9.1 Hawking radiation

　　9.1.1 Schwarzschild solution

　　9.1.2 Kruskal-Szekeres coordinates

　　9.1.3 Field quantization and Hawking radiation

　　9.1.4 Hawking effect in 3 + 1 dimensions

　　9.2 Therroodynamics of black holes

　　9.2.1 Laws of black.hole thermodynamics

　10 The Casimir effect

　　10.1 Vacuum energy betw.een plates

　　10.2 Regularization and renormalization

Part II Path integrals and vacuum polarization

　11 Path integrals

　　11.1 Evolution operator. Propagator

　　11.2 Propagator as a path integral

　　11.3 Lagrangian path integrals

　　11.4 Propagators for free particle and harmonic oscillator

　　11.4.1 Free particle

　　11.4.2 Quadratic potential

　　11.4.3 Euclidean path integral

　　11.4.4 Ground state as a path integral

　12 Effective action

　　12.1 Driven harmonic oscillator (continuation)

　　12.1.1 Green's functions and matrix elements

　　12.1.2 Euclidean Green's function

　　12.1.3 Introducing effective action

　　12.1.4 Calculating effective action for a driven oscillator

　　12.1.5 Matrix elements

　　12.1.6 The effective action "recipe"

　　12.1.7 Backreaction

　　12.2 Effective action in external gravitational field

　　12.2.1 Euclidean action for scalar field

　　12.3 Effective action as a functional determinant

　　12.3.1 Reformulation of the eigenvalue problem

　　12.3.2 Zeta function

　　12.3.3 Heat kernel

　13 Calculation of heat kernel

　　13.1 Perturbative expansion for the heat kernel

　　13.1.1 Matrix elements

　　13.2 Trace of the heat kernel

　　13.3 The Seeley-DeWitt expansion

　14 Results from effective action

　　14.1 Renormalization of the effective action

　　14.2 Finite terms in the effective action

　　14.2.1 EMT from the Polyakov action

　　14.3 Conformal anomaly

Appendix 1 Mathematical supplement

　A1.1 Functionals and distributions (generalized functions)

　A1.2 Green's functions, boundary conditions, and contours

　A1.3 Euler's gamma function and analytic continuations

Appendix 2 Backreaction derived from effective action

Appendix 3 Mode expansions cheat sheet

Appendix 4 Solutions to exercises

Index