Dyson-Schwinger Equations and their Applications to QCD.pdf

1、索取號：鯉3塵3』：!i3密級：公玨南京矸乾火籮碩士學位論文Dyson——SchwingerEquationsandtheirApplicationstoQCD作者：院系：石遠美物理科學與技術(shù)學院指導教師：平加倫教授學科專業(yè)：理論物理園AbstractConfinementandthedynamicalchiralsymmetrybreakingarethetwogenuineeffectsofnon—perturbativeQCD(N

2、PQCD)Tostudythesetwoeffects，non—perturbativemethodsarerequiredRecentlytheDyson—Schwinger(DS)approachhasbeenausefultooltostudythesetwoeffects(1，2，3】Ithasbeenproventobesuccessfulindevelopingahadronphenomenologywhichinterpo

3、latessmoothlybetweentheinfrared(nonperturbative)andtheultraviolet(perturbative)regime【1，2，3】Inthispaper，wefirstlyintroducebrieflytheDSequation(DSE)formalismandthenusetheDSapproachintwoaspectsofnonperturbativestudiesinthe

4、studyoftheinfraredbehaviorofghionandghostpropagatorsinthecoupledgluonandghostDSEs，wherethethreegiuonandghost垂uonvertexfunctions8zetakentobebare，weusetwoapproachestodenormalization：theanalyticcontinuationapproachandthesub

5、tractionapproachTheresultsshowthatthetworenormalizationapproachesgivethesaIneresults(K_1，＆(o)=419)intheinfraredanalysisofpropagatorsThenwedotheinfraredanalysisusingaspecialchoiceofthreegluonandghostgiuonvertexfunctionswh

6、icharederivedbytheirSlavnovTayloridentities(STIs)【3，4】OurcalculationsshowthattheverticesusedinRefs【3，4】arenot”full”ones，becauseifwedoexactintegrationsofthefunctions，nosolutionof^existsInstudyingthelinearresponseofthedres

7、sedquarkpropagatorinthepresenceofthevariableexternalfield，wederiveageneralexpressionforthevacuulnsusceptibilitycalculationintheQuantumChromodynamical(QCD)sumruletwopointexternalfieldformulausingthevariableaxialexternalfi

8、eldasanexampleTheexpressionswehavederivedforthecalculationofvacuumsusceptibilityaremodelindependentThenweusetheexpressionstothecalculationoftheaxialvector，vectorandtensorvacuunlsusceptibilitiesThenumericulvaluesofthethre

9、eyscuulususceptibilitiesarecalculatedwithinthefraxneworkoftherainbow—ladderapproximationoftheDSapproachAcomparisonwiththeresultsofthepreviousapproachisgivenWeshowthatthedifierencesbetweentheresultsofourapproachandtheprev

10、iousfortheaxialvectorandvectorvacuumsusceptibilitiesarelarge，whilethatforthetensorvaCUUlTIsusceptibilityissmallThedifierencesrootinthedressedeffectsofthenonperturbativeverticesKeywordsDysonSchwingerapproach，infraredbehav