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[德] 马克翰维 著 / 世界图书出版公司 / 2010-04 / 平装
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引力的量子效应导论(英文版)
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。
PrefacePartICanonicalquantizationandparticleproduction1Overview:atasteofquantumfields1.1Classicalfield1.2Quantumfieldanditsvacuumstate1.3Thevacuumenergy1.4Quantumvacuumfluctuations1.5Particleinterpretationofquantumfields1.6Quantumfieldtheoryinclassicalbackgrounds1.7Examplesofparticlecreation2Reminder:classicalandquantumtheory2.1Lagrangianformalism2.1.1Functionalderivatives2.2Hamiltonianformalism2.3QuantizationofHamiltoniansystems2.4HilbertspacesandDiracnotation2.5Operators,eigenvalueproblemandbasisinaHilbertspace2.6Generalizedeigenvectorsandbasicmatrixelements2.7Evolutioninquantumtheory3Drivenharmonicoscillator3.1Quantizinganoscillator3.2The"in"and"out"states3.3MatrixelementsandGreensfunctions4Fromharmonicoscillatorstofields4.1Quantumharmonicoscillators4.2Fromoscillatorstofields4.3Quantizingfieldsinaflatspacetime4.4Themodeexpansion4.5Vacuumenergyandvacuumfluctuations4.6TheSchrodingerequationforaquantumfield5Reminder:classicalfields5.1Theactionfunctional5.2Realscalarfieldanditscouplingtothegravity5.3Gaugeinvarianceandcouplingtotheelectromagneticfield5.4Actionforthegravitationalandgaugefields5.5Energy-momentumtensor6Quantumfieldsinexpandinguniverse6.1Classicalscalarfieldinexpandingbackground6.1.1Modeexpansion6.2Quantization6.3Bogolyubovtransformations6.4Hilbertspace;"a-andb-particles"6.5Choiceofthephysicalvacuum6.5.1Theinstantaneouslowest-energystate6.5.2Ambiguityofthevacuumstate6.6Amplitudeofquantumfluctuations6.6.1Comparingfluctuationsinthevacuumandexcitedstates6.7Anexampleofparticleproduction7QuantumfieldsinthedeSitteruniverse7.1DeSitteruniverse7.2Quantization7.2.1Bunch-Daviesvacuum7.3Fluctuationsininflationaryuniverse8Unruheffect8.1Acceleratedmotion8.2Comovingframeofacceleratedobserver8.3Quantumfieldsininertialandacceleratedframes8.4Bogolyubovtransformations8.5OccupationnumbersandUnmhtemperature9Hawkingeffect.Thermodynamicsofblackholes9.1Hawkingradiation9.1.1Schwarzschildsolution9.1.2Kruskal-Szekerescoordinates9.1.3FieldquantizationandHawkingradiation9.1.4Hawkingeffectin3+1dimensions9.2Therroodynamicsofblackholes9.2.1Lawsofblack.holethermodynamics10TheCasimireffect10.1Vacuumenergybetw.eenplates10.2RegularizationandrenormalizationPartⅡPathintegralsandvacuumpolarization11Pathintegrals11.1Evolutionoperator.Propagator11.2Propagatorasapathintegral11.3Lagrangianpathintegrals11.4Propagatorsforfreeparticleandharmonicoscillator11.4.1Freeparticle11.4.2Quadraticpotential11.4.3Euclideanpathintegral11.4.4Groundstateasapathintegral12Effectiveaction12.1Drivenharmonicoscillator(continuation)12.1.1Greensfunctionsandmatrixelements12.1.2EuclideanGreensfunction12.1.3Introducingeffectiveaction12.1.4Calculatingeffectiveactionforadrivenoscillator12.1.5Matrixelements12.1.6Theeffectiveaction"recipe"12.1.7Backreaction12.2Effectiveactioninexternalgravitationalfield12.2.1Euclideanactionforscalarfield12.3Effectiveactionasafunctionaldeterminant12.3.1Reformulationoftheeigenvalueproblem12.3.2Zetafunction12.3.3Heatkernel13Calculationofheatkernel13.1Perturbativeexpansionfortheheatkernel13.1.1Matrixelements13.2Traceoftheheatkernel13.3TheSeeley-DeWittexpansion14Resultsfromeffectiveaction14.1Renormalizationoftheeffectiveaction14.2Finitetermsintheeffectiveaction14.2.1EMTfromthePolyakovaction14.3ConformalanomalyAppendix1MathematicalsupplementA1.1Functionalsanddistributions(generalizedfunctions)A1.2Greensfunctions,boundaryconditions,andcontoursA1.3EulersgammafunctionandanalyticcontinuationsAppendix2BackreactionderivedfromeffectiveactionAppendix3ModeexpansionscheatsheetAppendix4SolutionstoexercisesIndex
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