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引力的量子效应导论
作者：（德）马克翰维 著
出版社：世界图书出版公司
出版时间：2010-04-01
ISBN：9787510005527
定价：¥45.00
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内容简介
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。阅读本书只需要基本的广义相对论知识。前言；（第一部分）正则量子化和粒子产生：概述：量子场；回顾：经典和量子理论；受迫谐振子；从谐振子到场；回顾：经典场；扩张宇宙中的量子场；Sitter宇宙中的量子场；Unruh效应；Hawking效应，黑洞热力学；Casimir效应；（第二部分）路径积分和真空极化：路径积分；有效作用量；热核计算；从有效作用量导出的结论；附录1：数学补充；附录2：反向反应的有效作用量推导；附录3：模展开要点；附录4：习题答案；索引。读者对象：理论天体物理，宇宙学，粒子物理和超弦理论等专业的高年级本科生、研究生和相关领域的科研人员。
作者简介
暂缺《引力的量子效应导论》作者简介
目录
Preface
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
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
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