introduction to quantum fields in curved spacetime and the hawking effect

《introduction to quantum fields in curved spacetime and the hawking effect》由会员上传分享，免费在线阅读，更多相关内容在学术论文-天天文库。

1、IntroductiontoQuantumFieldsinCurvedSpacetimeandtheHawkingEffectTedJacobsonDepartmentofPhysics,UniversityofMarylandCollegePark,MD20742-4111jacobson@physics.umd.eduAbstractThesenotesintroducethesubjectofquantumfieldtheoryincurvedspacetimeandsomeofitsapplicationsandthequestions

2、theyraise.Topicsincludeparticlecreationintime-dependentmetrics,quantumoriginofprimordialperturbations,Hawkingeffect,thetrans-Planckianquestion,andHawkingradiationonalattice.BasedonlecturesgivenattheCECSSchoolonQuantumGravityinValdivia,Chile,January2002.arXiv:gr-qc/0308048v3

3、9Apr20041Contents1Introduction42Plancklengthandblackholethermodynamics52.1Plancklength.................................52.2Hawkingeffect.................................62.3Blackholeentropy..............................73Harmonicoscillator84Quantumscalarfieldincurvedspacetim

4、e114.1Conformalcoupling..............................124.2Canonicalquantization............................134.3Hilbertspace.................................144.4Flatspacetime.................................154.5Curvedspacetime,“particles”,andstresstensor..............174

5、.6Remarks....................................184.6.1Continuumnormalizationofmodes.................184.6.2Masslessminimallycoupledzeromode...............195Particlecreation195.1Parametricexcitationofaharmonicoscillator...............205.1.1Adiabatictransitionsandgroundstate

6、...............215.1.2Suddentransitions..........................225.1.3Relationbetweeninandoutgroundstates&thesqueezeoperator225.2Cosmologicalparticlecreation........................245.3Remarks....................................275.3.1Momentumcorrelationsinthesqueezedva

7、cuum..........275.3.2Normalizationofthesqueezedvacuum...............275.3.3Energydensity............................275.3.4Adiabaticvacuum...........................275.4deSitterspace................................285.4.1Primordialperturbationsfromzeropointfluctuations....

8、...286Blackholeevaporation306.1Historicalsketch................................3026.2TheH