a primer on instantons in qcd

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1、APrimeronInstantonsinQCDHilmarForkelInstitutfur•TheoretischePhysik,Universit•atHeidelberg,Philosophenweg19,D-69120HeidelbergGermanyAugust2000Thesearetheextendednotesofasetoflecturesgivenatthe12thWorkshoponHadronicInteractions"attheIF/UERJ,RiodeJaneiro(31.

2、5.-2.6.2000).Thelecturesaimatintroducingessentialconceptsofinstantonphysics,withemphasisontheroleofinstantonsingeneratingtunnelingamplitudes,vacuumstructure,andtheinducedquarkinteractionsassociatedwiththeaxialanomaly.Afewexamplesfortheimpactofinstantonsont

3、hephysicsofhadronsarealsomentioned.arXiv:hep-ph/0009136v111Sep2000Contents1Introduction21.1Motivationandoverview.......................................21.2WKBreminder............................................32Instantonsinquantummechanics42.1SCAviapathin

4、tegrals........................................42.1.1Thepropagatorforrealtimes:pathintegralandSCA..................42.1.2Propagatorinimaginarytime................................62.1.3Pathintegralinimaginarytime:tunnelinginSCA....................72.1.4Sadd

5、lepointapproximation.................................92.2Doublewell(hill)potentialandinstantons.............................102.2.1Instantonsolution......................................102.2.2Zeromode...........................................122.2.3Dilut

6、einstantongas.....................................132.3Periodicpotential...........................................163InstantonsinQCD183.1VacuumtopologyandYang-Millsinstantons............................183.1.1TopologyoftheYang-Millsvacuum.................

7、...........183.1.2Yang-Millsinstantonsolution................................223.2Includingquarks...........................................233.2.1Theaxialanomaly......................................243.2.2Quarkzeromodes...................................

8、...263.3Instantontopologyandthetavacua................................273.3.1Instantontopologyandself-duality.............................273.3.2Thevacuumangle......................................294Outlook: