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Noncommutative gauge theory beyond the canonical case [Elektronische Ressource] / vorgelegt von Wolfgang Behr

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PhNoncommorgelegtutativersit?teolfgangGaugederTheoryhenboneyJuliondysiktheLudwigMaximiliansUnivCanonicalM?ncCasevDissertationvderWFBehrakult?t2005f?rSacTeiteragJuliusderProf.mProf.?ndlicesshenhPr?fung:Iv3.ter:NoDr.vWemzwbGutacerter:2005Dr.ersteroGutachsh?∂ (f?g)=∂f?g+f?∂ gi i i?ductmostThere,commonlygaugestudiedwnoncommtoutativcorrespearespace.eNoncom-inmulateutativableepartgaugearoundtheoriesalgebra),thatgohacanonicalvhealuedordinaryedgaugenonconstantheorycommasthetheirycommgaugeutativgrounde.limitk-spacehaofvmatricesecommbtheeenniteconstructedethere.wButandtheselinkingtheorieseins)hapvgaugeeytheireddraWwbacde-ks:quanFirsteofmaps.all,studyconstanmatrixtenoncommmatrixutativitcreatingycasecantheonlythebnewithantheoryapprogaugeximation4-dimensionalofandamatcrealistictontheoryinstan,-andcanthereforemittheisynecessarycanonicaltotostudyelds.morederivcomplicated(viel-space-depaendenitttostructuresutativasthatwnoncommell.goSecondlyon,ininethearecanonicalexpresscase,endencetheutativnoncommonutativitcommyterpartsdidn'tSeibfulllthetheeinitialutativhopineapproacofnoncommcuringistheofdivtheergenciesgroundofgaugequanthetummatriceseld(theytheoryo.tationThere-bforetoitbisespvergencies.eryconstructdesirablenitetospaces).understandisnoncommonutativineespacesalsothatablereallypartsadmitwnniteofQFTwiths.ofThese.

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Published 01 January 2005
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PhNoncommorgelegtutativersit?teolfgangGaugederTheoryhenboneyJuliondysiktheLudwigMaximiliansUnivCanonicalM?ncCasevDissertationvderWFBehrakult?t2005f?rSacTeiteragJuliusderProf.mProf.?ndlicesshenhPr?fung:Iv3.ter:NoDr.vWemzwbGutacerter:2005Dr.ersteroGutachsh?
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?
ductmostThere,commonlygaugestudiedwnoncommtoutativcorrespearespace.eNoncom-inmulateutativableepartgaugearoundtheoriesalgebra),thatgohacanonicalvhealuedordinaryedgaugenonconstantheorycommasthetheirycommgaugeutativgrounde.limitk-spacehaofvmatricesecommbtheeenniteconstructedethere.wButandtheselinkingtheorieseins)hapvgaugeeytheireddraWwbacde-ks:quanFirsteofmaps.all,studyconstanmatrixtenoncommmatrixutativitcreatingycasecantheonlythebnewithantheoryapprogaugeximation4-dimensionalofandamatcrealistictontheoryinstan,-andcanthereforemittheisynecessarycanonicaltotostudyelds.morederivcomplicated(viel-space-depaendenitttostructuresutativasthatwnoncommell.goSecondlyon,ininethearecanonicalexpresscase,endencetheutativnoncommonutativitcommyterpartsdidn'tSeibfulllthetheeinitialutativhopineapproacofnoncommcuringistheofdivtheergenciesgroundofgaugequanthetummatriceseld(theytheoryo.tationThere-bforetoitbisespvergencies.eryconstructdesirablenitetospaces).understandisnoncommonutativineespacesalsothatablereallypartsadmitwnniteofQFTwiths.ofThese.thetprowalgebraobaspgaugedectsucofingoingsamebaeyasondthethecasecanonicalleadcasefunction-vwillgaugebByethetheationsmainframesfobcusofofcurvthismanifold,thesis.isTheyossiblewillformbnoncommeeaddressedtheorieswithinadmitttwutativitoanddierentottheoryformalisms,curveacspacetimehtheofutativwhiclimit.heisalsoesptoeciallythesuitedpforofthenoncommpurpeose.titiesIntheirtheondingrstutativpartcounnoncommbutativusingeerg-WittenspacesIncreatedsecondbwywillanoncomm-proeductstheoryarethestudied.theoryInh.thethecaseutativofspacenonconstanthetstatenoncommautativitaction,yuctuations,thisthestateordinarythederivtheoryativInescanonicalptheossessusedainnite-dimensionaldeformedareLeibnizFrule,ci.e.represenisofisHeisenordinatesergcoleadingoawumter6problems,ofeciallyutatordivt,Thereforecommethegaugewhereusingspacetime,dimensionaldeformed(fuzzyCanonicallyThisAbstracttheoryconstannite,esgaugetoiiitheoryusedaregularizemanifoldnoncommtheeutativtheorylimitthecancase.bparticular,eto.theThereforeutativwgaugeeofconstructcanonicalnewInobwjectsarethattostillhhaofvknoeinstanansectorundeformedtheLeibnizcaserule.theThesetonsderivtheationstheoryofthetogethervgroupAoncMPIknooard,wledgementhesis,tseIywofanandtmaterialtoeryexpressrelaxedmbutyduringgratitudeentofronallblacthosefruitfulwhocollabmadeofthisinthesisandpinossible.theIproespandeciallyleastwfundinganlasttsptotthankinProf.tDr.theJuliuskbWtheessdiscussionsfortheirhisorationguidancepartsandthesteadyincludedsuppthisort,allAndreasevSykoneora,theFforrankcongenial,MeyanderductivandatmosphereHaroldlastSteinacnotktheerforformethethesemanthreeyears.hours?
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