Springer.Kopietz.P.Bosonization.of.interacting.fermions.in.arbitrary.dimensions.(LNP.m48.Springer.1997)(ISBN.3540627200)(286s)

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1、PrefaceInthisbookwedescribeanewnon-perturbativeapproachtothefermionicmany-bodyproblem,whichcanbeconsideredasageneralizationtoarbitrarydimensionsofthewell-knownbosonizationtechniqueforone-dimensionalfermions.Ourapproachisbasedonthedirectcalculationofcorrelationfun

2、ctionsofinteractingFermisystemswithdominantforwardscatteringviafunctionalintegrationandHubbard-Stratonovichtransformations–wedonotattempttogeneralizeone-dimensionaloperatoridentitiesbetweenthefermionicandbosonicfieldoperatorstohigherdimensions.Thefundamen-talideas

3、ofhigher-dimensionalbosonizationhavefirstbeenformulatedbyA.Luther(1979)andbyF.D.M.Haldane(1992).InthisbookweshallgobeyondtheseideasanddevelopapowerfulandsystematicmethodforbosonizinginteractingfermionsonacurvedFermisurface.Wethenapplyourmethodtoanumberofproblemsof

4、physicalinterestwhichareverydif-ficult–andinsomecasesimpossible–tosolvebymeansofconventionaldiagrammaticperturbationtheory.Therestrictiontodominantforwardscatteringmeansthatinrealspacetheeffectiveinteractionbetweenthefermionsmustbesufficientlylong-range.Physicalexamp

5、lesaretheCoulombinteractionathighdensities,ortheef-fectivecurrent-currentinteractionmediatedbytransversegaugefields.Ontheotherhand,short-rangeinteractionslikethelocalHubbard-interactioncannotbedirectlytreatedwithinourapproach.Itseems,however,thatourmethodcanbegene

6、ralizedtoinclude(atleastperturbatively)scatteringpro-cesseswithlargemomentumtransfer.AlthoughweshallrestrictourselvestonormalFermisystems,withourfunctionalapproachitshouldbestraightfor-wardtotakealsospontaneoussymmetrybreakingintoaccount.Wewouldliketoencourageint

7、erestedreaderstocontributetothefurtherdevelopmentofourmethod.Attheendofeachchapterwehavethereforementionedopenresearchproblems,whichmightbesolvablewiththehelpofextensionsofthemethodsdevelopedinthisbook.Iwouldliketothankatthispointeveryonewho–directlyorindirectly–

8、hashelpedmetocompletethisbook.Firstofall,IamgratefultoKurtSch¨onhammerfornumerouscollaborationsanddiscussions,forgettingmeinterestedinbosonizationshortlyafterI