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1、Ú264'Ú4ÚßÜïíëËïívd.26,N£.42002ê4ÂÄGHENERGYPHYEI·ANDNUCIZARPHYSECSAF-,émNewRealizationofN=2SupersymmetricQuantumMechanicsandShapehvarianceMedinaAblikimEHIJANGWei--Chez382l(InstitutedHú,EnerwPhysics,ö,eChine-eAcademydSciegee-,BeijiEHE1©²",China)2(ImtutedAwtidOEms®,XiÐimgumv¥,®,UEmqimØ46.Gin-)AMMct
2、'ITEenewsuperehaªegmconsbmetedandtheweighthdoniadehedto¢dytheN=2one-dimensionalSEEpemymmemequanMnmechanics.severaleÊraPIesamamu--edMtbenàreaHó-tlOE1.KeyWOE-daquantummechmica,HamiltonianHeramÅ,schzedingerequaum,shapeanvarzance1IntrodEEdomWhilestudyingthedynamicalbmakingofsupersymmetry,in1981Wiuen
3、lljconstructedasim-pk,butnottdvialmodel-»-SEEpemyzymetdcqumummeetmics(sgQM)½,nmelyasysMdNHemIitiansupemhazÅesQi(i=1,2,•,N)andSEEpemymmetricHamiltonianH,satisfyingthefollowingEªElations:i¶,Qji=2HSe,[¶,H]=0,Q:=Qi(i=1,2,•,N).(1.1)FortheN=2case,Eq.(1.1)cmhexpressedaltemauvely,iQ+,Q-
4、;=2H,Q:=0,[QÃ,H]
5、=0,Q:=Q.,(1.2)byintroducingð=÷(Q1ÁiQz)(13)'IEepmblemofconstmctingthemalizationmmimpOEtantoneinstudyof·QM.Inone-dimension-dazzdN=2cases,themalizationdSSQMincommonuseisgivenbythefollowingfom1ofsuper-charges:ð=
6、ó¹+W(z)
7、ó,(14)LUª»andthesupersymmetricHamiltonianiss1idLW'--l-?Å+WlI+»-6Ö,(1.5)21dõ123,w
8、hereW(x)isthesupeEpotentialandthePadmauteesamevenbyi011-iOOKó=Â(Ò1óiÒ2),õ=ll,Ò=ll(16)É001É101Reedved5July2Þ1,Revmed25October«¡-supportedbyScieatihb,emhFomdationforReMmedsebo»,dsuteEdue-60nMini-tzydChin-338-345Ú4Ú®é'¤¢¼¦Ë¾ÈzNz2éÔÆ¿Óª¿Ä'àµÖÍδ»äÔ339Herewemll¢dyanewkinddrealigation,which×llincludem
9、mÁê,deaùdm-d.menSionalnonrelativisticqumumBEechmealsyaemintheframewoEtOSN=2SSQM(sedm2)-WewillaudythemlevantHamiltonimHeramhyandshapeinvadmee(sedon3)mdsomeexam-ples(section4).2NewRealizationRecentlymaudiedmanewredmuon¶SQ±'].suzmghmthegeneralimdmpepchazÃesddQI=(M161+NeJE+keI+ì,Q2=(RIÐ+Sez)E+YK+VÖ,
10、(2.1),øereM,N,K,L,R,S,T-ndVm(££ëlamFaeal)×netiomdz.Fmmtbealeebm-icamØmdS•ý,namelyQi=Qi=Hand
11、Q1,Q2
12、=0,màobtaintherelationsamongthoeehEEEdom:Case(a)S=M,R=-N,T=-L,V=K;Case(b)S=-M,R=N,T=L,V=-K;(2.2)c..dc)N=iM=óis=áR,T=áL,V=îkaCa