资源描述：
《Notes on Green’s Functions Theory for Quantum Many-Body Systems.pdf》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、NotesonGreen’sFunctionsTheoryforQuantumMany-BodySystemsCarloBarbieriTheoreticalNuclearPhysicsLaboratoryNishinaCenterforAccelerator-BasedScience,RIKENApril2009LiteratureAmodernandcompresensivemonographyis•W.H.DickhoffandD.VanNeck,Many-BodyTheoryExposed!,2nded.(WorldScientific
2、,Singapore,2007).ThisbookcoversseveralapplicationsofGreen’sfunctionsdoneinrecentyears,includingnuclearandelectroncicsystems.Mostthematerialoftheselecturescanbefoundhere.Twopopulartextbooks,thatcoverthealmostcompleteformalism,are•A.L.FetterandJ.D.Walecka,QuantumTheoryofMany
3、-ParticlePhysics(McGraw-Hill,NewYork,1971),•A.A.Abrikosov,L.P.GorkovandI.E.Dzyaloshinski,MethodsofQuantumFieldTheoryinStatisticalPhysics(Dover,NewYork,1975).Otherusefulbooksonmany-bodyGreen’sfunctionstheory,include•R.D.Mattuck,AGuidetoFeynmnanDiagramsintheMany-BodyProblem,
4、(McGraw-Hill,1976)[reprintedbyDover,1992],•J.P.BlaizotandG.Ripka,QuantumTheoryofFiniteSystems(MITPress,CambridgeMA,1986),•J.W.NegeleandH.Orland,QuantumMany-ParticleSystems(Ben-jamin,RedwoodCityCA,1988).2Chapter1Preliminaries:BasicFormulaeofSecondQuantizationandPicturesMany
5、-bodyGreen’sfunctions(MBGF)areasetoftechniquesthatoriginatedinquantumfieldtheorybuthavealsofoundwideapplicationstothemany-bodyproblem.Inthiscase,thefocusarecomplexsystemssuchascrystals,molecules,oratomicnuclei.However,many-bodyGreen’sfunctionsstillsharethesamelanguagewithel
6、ementaryparticlestheory,andhaveseveralconceptsincommon.Toapplythisformalism,oneneedstouseofthecre-ation/destructionoperatorsofsecondquantizationandtheHeisenbergandinteractionpicturesofquantummechanics.Thepurposeofthischapteristogatherthebasicresultsofsecondquan-tizationand
7、pictures,sothattheycanbeusedforreferencelateron.Onetheway,wewillintroducesomeofthenotationtobeusedinourdiscussions.1.1ANoteonSingle-ParticleIndicesThefollowingconventionswillbeusedinmostofthesenotes.Whenneeded,theboldfacerwillbeusedtorefertothepositionofparticlesincoordina
8、tespaceandkformomentumspace.Wheninternaldegreesoffreedomarepresent,x≡(r,σ,τ,...)willbeuse
