Gentile統(tǒng)計的算符實現(xiàn)及應(yīng)用.pdf

1、天津大學(xué)碩士學(xué)位論文Gentile統(tǒng)計的算符實現(xiàn)及應(yīng)用姓名：沈堯申請學(xué)位級別：碩士專業(yè)：理論物理指導(dǎo)教師：戴伍圣20070101ABSTRACTGentilestatisticsisakindofintermediatestatisticsbetweenBoseEinstein刪isticsandFermiDiracstatisticsItisknownthatnaturerealizesonlytWOkindsof口articles：

2、oneobeysBoseEinsteinstatisticsandtheotherobeysFermiDiracstatistics；themaximumoccupationnumberofonequantumstateinthesetwokindsofstatisticsiSOOor1respectivelyInGentilestatistics，howeverthemaximumoccupationnumber，denotedbyn

3、，Callbechosenarbitrarilybetweenooand1Therelationsofcreationandannihilationoperatorsofbosonsarecommutativeandoffermionsareanticon】mutative。TherelationsofcreationandannihilationoperatorscorrespondingtoGentilestatisticsCall

4、beexpressedbythenbracketThecommutativityandtheantic：ommutativitywillbethetwolimitcasesofthenbracketAsemphasizedabove，theonlykindsofparticleswhichappearinnatureareeitherbosonsorfermions，SOtheparticlesobeyingGentilestatist

5、icsmustnotberealparticlesAsalleffectivemethod，however，theintroductionofsuchimaginaryparticlescanbeusedtodealwithsomecomplexinteractionsystemsThispaperfallsintofiveparts，plusanintroductionandconclusionThefirstpartdiscusse

6、sthegeneralpropertiesofthenbracketBasedontheseresults，wealsoprovidesomegeneralrelmionsforcommutativeandanticommutativebracketsbysetting以=ooand船=1ThesecondpartfocusesonthecreationandannihilationoperatorscorrespondingtoGen

7、tilestatisticsThethirdpartseekstoconstmcttheGentilestatisticsoscillatorsandcalculate也eirenergyspectraSuchoscillatorswillreturrltoBoseandFermioscillatorswhen玎=oOand珂21，respectivelyThefourthpartintroducesthecoherentstateco

8、rrespondingtoGentilestatisticsThefifthpartsuggestssomeschemesoftherepresentationofangularmomentum(su(2))algebrabasedonGentilestatisticsIntheserepresentations，theangularmomentumalgebracanberepresentedbyasinglesetofcreatio

9、nandannihilationoperatorsNoticethatintheSchwingerrepresentationtwoindependentsetsofbosonoperatorsareused，andtheHolsteinPrimakoffrepresentation，thoughonlvusesasinglesetofcreationandannihilationoperators，isnotreallyabosoni