Bose Description of Pauli Spin Operators and Related Coherent State

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1、Commun．Theor．Phys．(Beijing，China)43(2005)PP．17—21⑥InternationalAcademicPublishersVo1．43，No．1，January15，2005BoseDescriptionofPauliSpinOperatorsandRelatedCoherentStatesJIANGNian—Quan，，FANHong—Yi，，。andLUHai—Liang。lDepartmentofPhysicsWenzhouNormalCollege，W

2、enzhou325027，China，2DepartmentofMaterialScienceandEngineeringUniversityofScienceandTechnologyofChina，Hefei230026，China，3DepartmentofPhysics，ShanghaiJiaoTongUniversity，Shanghai200030，China(ReceivedDecember22，2003)AbstractUsingboththefermionic—likeandthe

3、bosonic—likepropertiesofthePaulispinoperatorso-+，o一，ando：wediscussthederivationofBosedescriptionofthePaulispinoperatorsoriginallyproposedbyShigefumiNaka，anddeduceanothernewbosonicrepresentationofPaulioperators．Therelatedcoherentstates，whicharenonlinear

4、coherentstateandcoherentspinstatesfortwospins，respectively,areconstructed．PACSnumbers：03．65．CaKeywords：BosedescriptionofPaulispinoperators，nonlinearcoherentstate，coherentspinstate1Introductiontheanti—commutingoperatorscanberealizedastheop-Thepurposeoft

5、hispaperistodiscussthesingle—eratorshavingmatrixelementsbetweenthesesubspaces．modeBosedescriptionofPaulispinoperators，asoneBysettingcanseeshortlylater．thatthisdescriptionisdifierentfromtheSchwingertwo-modeBoserealizationofangu—(at)+10)=I2n+1)larmomentu

6、m．【lJwhilethefclrmerisonlyvalidforspinJ(2n+1111／2，thelatterappliesforanyvaluesofangularmomen—n，2)=(at)10)=I2n)(4)turn．TheBosedescriptionofPaulispinoperatorswas、／／(2n)!originallyproposedbyShigefumiNaka．ItcanalsobeappliedtotheFermioperators，sincethequant

7、izationofinFockspace，whereIn)=(at／佩)10)istheFockstatetheanti．．commutingvariablesbyusinganti．commutatorsandnotingthatgeneratestheelementsofClifordalgebrasuchasPauliNmatrices．ToseetheexactresemblancebetweenFermiop—COS‘——∞∑2n)(2n(5)2eratorsandthePaulispin

8、operatorsmoreclearly，weusethe2×2matrixreDresentationoftheFermioperators．LetShigefumiNakaidentifiedfandftbefermionannihilationandcreationoperatorsrespectively,satisfyinganti—commutativerelations而cos2(nN／2)、／Ⅳ+1。：I’2n)“(2n+1{f，ft}+=1，f=0，