An introduction to QED & QCD (2008)

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1、AnIntroductiontoQED&QCDN.J.EvansDepartmentofPhysicsandAstronomyUniversityofSouthamptonSouthamptonSO171BJLecturespresentedattheSchoolforHighEnergyPhysicists,September2008.1IntroductionTheaimofthiscourseistoteachyouhowtocalculatetransitionamplitudes,crosssectionsa

2、nddecayrates,forelementaryparticlesinthehighlysuccessfultheoriesofQuantumElectrodynamics(QED)andQuantumChromodynamics(QCD).MostofourworkwillbeinunderstandinghowtocomputeinQED.BytheendofthecourseyoushouldbeabletogofromaFeynmandiagram,suchastheoneforee!ingu

3、re5,toanumberforthecrosssection.Todothiswewillhavetolearnhowtocopewithrelativistic,quantum,particlesandanti-particlesthatcarryspin.Infactallthesepropertiesofparticleswillemergeratherneatlyfromthinkingaboutrelativisticquantummechanics.TherulesforcalculatinginQCDa

4、reslightlymorecomplicatedthatinQED,aswewillbrie yreview,however,thebasictechniquesforthecalculationareverysimilar.Wehavealottocoversowillnecessarilyhavetotakesomeshortcuts.OurmainfudgewillbetoworkinrelativisticquantummechanicsratherthanthefullQuantumFieldTheory(

5、QFT)(sometimesreferredtoas`secondquantization').WewillbeingoodcompanythoughsincewewilllargelyfollowmethodsfromFeynman'spapersandtextbookssuchasHalzenandMartin.InquantummechanicsaclassicalwaveisusedtodescribeaparticlewhosemotionissubjecttotheUncertaintyPrinciple.

6、InafullQFTthewave'smotionitselfissubjecttotheUncertaintyPrincipletoo-thequantaofthateldarewhatwethenrefertoasparticles.Luckilyatlowestorderinaperturbationtheorycalculationoneneglectsthequantumnatureoftheeldandthetwotheoriesgivethesameanswer.Athigherordersthequ

7、antumnatureoftheeldgivesrisetovirtualpaircreationofparticles-inthequantummechanicsversionofthestorytheseareincludedinamoreadhocfashionaswewillsee.LuckilythesimultaneousQFTcoursewillgiveyouagoodgroundinginmoreprecisemethodologies.Thusourstartingpointwillbeordina

8、ryQuantumMechanicsandourrstgoal(section2)willbetowritedowna`relativisticversion'ofQuantumMechanics.Thiswillleadustolookatrelativisticwaveequations,inparticulartheDir