ABSTRACT
Becauseoftranslationalinvarianceinspaceandtime,Mdependsonly onthedifferencex-x"'.WecanthusdefineitsFouriertransform M(k,w)exactlyaswedidforG(k,w).Aftertransformingequation(4-4), wegettheverysimpleresult
[2~-w-M(k,w)]G(k,w)=1(4-8) ThepolesofGwillthusbetherootsofthefactor[k2/2m-w-M(p)]. Thisimportantresultwillultimatelyyieldthequasi-particleenergy. M(p)iscalledthe"self-energy,"or"mass,"operator.Weshallmeetit againinChap.5,intheframeworkofperturbationtheory,whereithas averysimplegraphicalinterpretation.
