缺陷的拓撲場論在物理學前沿中的應用.pdf

1、蘭州大學碩士學位論文缺陷的拓撲場論在物理學前沿中的應用姓名：司鐵巖申請學位級別：碩士專業(yè)：理論物理指導教師：段一士20050401ABSTRACTInthisdissertation，applyingProfessorDuan’s出mappingtopologicalcurrenttheory，westudiedthetopologicaldefectsonthecompactclosedbiologicalmem—branesandt

2、hevortexexcitationintopologicalquantummechanics，F(xiàn)irstlywepresentthe出mappingtopologicalcurrenttheoryintermofDeRahmcurrent，thetopologicalcurrenttheoryisexpressedintothreecompactclearformulasWealsogiveabriefintroductiontoth

3、ebifurcationtheoryofthetopologicalcurrentSecondly，weintroducedtheSO(2)gaugefieldtheoryonthemembranesurfaceandexpresstheS0(2)gaugepotentialastheunitorderparameterofthemembraneUsingtheso(2)gaugepotentialdecompositiontheory

4、，wedefinedtheuo)gaugepotentialandexpressedtheGaussiancurvatureastheU(1)gaugefieldtensorintheframeworkofthevielbeintheoryThenapplyingProfessorDuan’8出mappingtopologicalcurrenttheory，itisshownthatthesumofthewindingnumbersof

5、thedefectsonthemembraneistheEulercharacteristicnumberMoreover，wediscussedthedistributionoftopologicaldefectsontheaxisymmetricmembranesurfacesOnthesphericalmembrane，thesumofthewindingnunlbersofthedefectsequals2，thegrounds

6、tateisfourdefectswithW=1／2，theysitattheverticesofatetrahedronThefirstexcitedstateistwodefectswithW=1theysitattheSouthPolepointandNorthpolepointofthesphereThesecondexcitedstateisonedefectswithW=2，itsitseverywhereThebiconc

7、avediscoidishomcomorphictoasphere，SOithasasimilardistribution，thetwodefectswithW=liustsitsattheSouthPolepointandNorthpolepointFurthermore，whiletakingintoaccountoftheanomalouscoupling，westudiedthedefectsonthebiconcavesurf

8、aceoftheredbloodcellAsforatOrtLswhoseEulernumberisOsothegroundstateofthetoru8ustcorrespondstotheeaseofnodefectsThirdly，UsingProfessorDuan’8仁mappingtopologicalcurrenttheory，westudythevortexexcitationintopologicalquantumme

9、chanics，theinnertopologicalstructureofthevortexexcitationispresentedwealsoanalyZCthedistributionofthevortexexcitationinthesphericalpotentialwellandharmonicoscillatorwellAc—cordingtothetopologicalquantummechanics，thevorte