Many-body quantum theory in condensed matter physics An introduction.pdf

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1、IntroductiontoMany-bodyquantumtheoryincondensedmatterphysicsHenrikBruusandKarstenFlensbergØrstedLaboratory,NielsBohrInstitute,UniversityofCopenhagenMikroelektronikCentret,TechnicalUniversityofDenmarkCopenhagen,15August2002iiPrefacePrefaceforthe2001editionThisintroductiontoquantumfieldtheor

2、yincondensedmatterphysicshasemergedfromourcoursesforgraduateandadvancedundergraduatestudentsattheNielsBohrInstitute,UniversityofCopenhagen,heldbetweenthefallof1999andthespringof2001.Wehavegonethroughthepainofwritingthesenotes,becausewefeltthepedagogicalneedforabookwhichaimedatputtinganemp

3、hasisonthephysicalcontentsandapplicationsoftheratherinvolvedmathematicalmachineryofquantumfieldtheorywithoutloosingmathematicalrigor.Wehopewehavesucceededatleasttosomeextendinreachingthisgoal.Wewouldliketothankthestudentswhoputupwiththefirstversionsofthisbookandfortheirenumerableandvaluable

4、commentsandsuggestions.WeareparticularlygratefultothestudentsofMany-particlePhysicsI&II,theacademicyear2000-2001,andtoNielsAsgerMortensenandBrianMøllerAndersenforcarefulproofreading.Naturally,wearesolelyresponsibleforthehopefullyfewremainingerrorsandtypos.DuringtheworkonthisbookH.B.wassup

5、portedbytheDanishNaturalScienceRe-searchCouncilthroughOleRømerGrantNo.9600548.ØrstedLaboratory,NielsBohrInstituteKarstenFlensberg1September,2001HenrikBruusPrefaceforthe2002editionAfterrunningthecourseintheacademicyear2001-2002ourstudentscameupwithmorecorrectionsandcommentssothatwefeltanew

6、editionwasappropriate.Wewouldliketothankoureverenthusiasticstudentsfortheirvaluablehelpinimprovingthisbook.KarstenFlensbergHenrikBruusØrstedLaboratoryMikroelektronikCentretNielsBohrInstituteTechnicalUniversityofDenmarkiiiivPREFACEContentsListofsymbolsxii1Firstandsecondquantization11.1Firs

7、tquantization,single-particlesystems...................21.2Firstquantization,many-particlesystems...................41.2.1Permutationsymmetryandindistinguishability............51.2.2Thesingle-particlestatesasbasisstates................61.2.3Operatorsinfirstquantizati