introduction to quantum field theory in condensed matter physics - flensberg,bruus

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ntroductiontouantumeldtheoryincondensedmatterphysicsHenrikBruusandarstenFlensbergrstedaboratoryielsBohr
nstituteCopenhagen,1September2001iiContents1Firstandsecondquantization31.1Firstquantization,single-particlesystems...................41.2Firstquantization,many-particlesystems

2、...................61.2.1ermutationsymmetryandindistinguishability............61.2.2Thesingle-particlestatesasbasisstates................71.2.3peratorsinrstquantization.....................91.3Secondquantization,basicconcepts......................111.3.1Theoccupationnumberrepresent

3、ation.................111.3.2Thebosoncreationandannihilationoperators............121.3.3Thefermioncreationandannihilationoperators...........141.3.4Thegeneralformforsecondquantizationoperators..........161.3.5Changeofbasisinsecondquantization.................171.3.6uantumeldoperators

4、andtheirFouriertransforms........191.4Secondquantization,specicoperators.....................201.4.1Theharmonicoscillatorinsecondquantization............201.4.2Theelectromagneticeldinsecondquantization...........211.4.3peratorsforkineticenergy,spin,density,andcurrent........231.4.4

5、TheCoulombinteractioninsecondquantization...........251.4.5Basisstatesforsystemswithdierentkindsofparticles.......261.5Secondquantizationandstatisticalmechanics.................271.5.1Thedistributionfunctionfornon-interactingfermions........301.5.2Distributionfunctionsfornon-interact

6、ingbosons...........301.6Summaryandoutlook..............................312Theelectrongas332.1Thenon-interactingelectrongas........................342.1.1Blochtheoryofelectronsinastaticionlattice............352.1.2on-interactingelectronsinthejelliummodel.............372.1.3on-intera

7、ctingelectronsatnitetemperature............402.2Electroninteractionsinperturbationtheory..................41st2.2.1Electroninteractionsin1orderperturbationtheory........43nd2.2.2Electroninteractionsin2orderperturbationtheory........452.3Electrongasesin3,2,1,and0dimensions............

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