引力的量子效应导论

出版时间：2010-4  出版社：世界图书出版公司  作者：马克翰维  页数：273  
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前言

This book is an expanded and reorganized version of the lecture notes for a course taught at the Ludwig-Maximilians University, Munich, in the spring semester of 2003. The course is an elementary introduction to the basic concepts of quantum field theory in classical backgrounds. A certain level of familiarity with general relativity and quantum mechanics is required, although .many of the necessary concepts are introduced in the text.The audience consisted of advanced undergraduates and beginning graduate students. There were 11 three-hour lectures. Each lecture was accompanied by exercises that were an integral part of the exposition and encapsulated longer but straightforward calculations or illustrative numerical results. Detailed solutions were given for all the exercises. Exercises marked by an asterisk （*） are more difficult or cumbersome.The book covers limited but essential material: quantization of free scalar fields; driven and time-dependent harmonic oscillators; mode expansions and Bogolyubov transformations; particle creation by classical backgrounds; quantum scalar fields in de Sitter spacetime and the growth of fluctuations; the Unruh effect;Hawking radiation; the Casimir effect; quantization by path integrals; the energy-momentum tensor for fields; effective action and backreaction; regularization of functional determinants using zeta functions and heat kernels. Topics such as quantization of higher-spin fields or interacting fields in curved spacetime, direct renormalization of the energy-momentum tensor, and the theory of cosmological perturbations are left out.The emphasis of this course is primarily on concepts rather than on compu-tational results. Most of the required calculations have been simplified to the barest possible minimum that still contains all relevant physics. For instance,only free scalar fields are considered for quantization; background spacetimes are always chosen to be conformally flat; the Casimir effect, the Unmh effect,and the Hawking radiation are computed for massless scalar fields in suitable 1 + 1-dimensional spacetimes. Thus a fairly modest computational effort suffices to explain important conceptual issues such as the nature of vacuum and parti-cles in curved spacetimes, thermal effects of gravitation, and backreaction. This should prepare students for more advanced and technically demanding treatments suggested below.The authors are grateful to Josef GalBner and Matthew Parry for discussions and valuable comments on the manuscript. Special thanks are due to Alex Vikman who worked through the text and prompted important revisions, and to Andrei Barvinsky for his assistance in improving the presentation in the last chapter.The entire book was typeset with the excellent LyX and TEX document prepa-ration system on computers running Debian GNU/Linux. We wish to express our gratitude to the creators and maintainers of this outstanding free software.Suggested literatureThe following books offer a more extensive coverage of the subject and can be studied as a continuation of this introductory course.N. D. BIRRELL and P. C. W. DAVIES, Quantum Fields in Curved Space （Cambridge University Press, 1982）.S. A. FULLING, Aspects of Quantum Field Theory in Curved Space-Time （Cambridge University Press, 1989）.

内容概要

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。

书籍目录

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

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《引力的量子效应导论(英文版)》是由界图书出版公司出版的。

用户评论 (总计8条)

•   学过量子场论后看看。需要有量子场论和广义相对论的基础。
•   这是世界图书出版公司引进的剑桥大学出版社的理论物理专著.适合物理专业研究生阅读.
•   也是蛮好的一本书，适合于硕士研究生一年的读者看。
•   孩子从中学到了很多知识。
•   该书的内容和讲述都令人满意。
•   非常喜欢，基本的入门书
•   前版本都是讲量子力学和场论的基础，对于专门搞这方面的人来说就显得多余，所以建议专业内的人别买，一共271页的书有120多页都是可以略过不看或者简要浏览的内容，真正有帮助的内容不多。
•   总体说来还不错，很详细