資源描述：
《The The Algebra of Grand Unified Theories》由會員上傳分享，免費在線閱讀，更多相關(guān)內(nèi)容在學(xué)術(shù)論文-天天文庫。
1、TheAlgebraofGrandUni?edTheoriesJohnBaezandJohnHuertaDepartmentofMathematicsUniversityofCaliforniaRiverside,CA92521USAMay4,2010AbstractTheStandardModelisthebesttestedandmostwidelyacceptedtheoryofelementaryparticleswehavetoday.Itmayseemcomplicatedandarbitrary,but
2、ithashiddenpatternsthatarerevealedbytherelationshipbetweenthree‘granduni?edtheories’:theoriesthatunifyforcesandparticlesbyextend-ingtheStandardModelsymmetrygroupU(1)×SU(2)×SU(3)toalargergroup.ThesethreeareGeorgiandGlashow’sSU(5)theory,Georgi’stheorybasedonthegr
3、oupSpin(10),andthePati–SalammodelbasedonthegroupSU(2)×SU(2)×SU(4).Inthisexpositoryaccountformathematicians,weex-plainonlytheportionofthesetheoriesthatinvolves?nite-dimensionalgrouprepresentations.Thisallowsustoreducetheprerequisitestoabareminimumwhilestillgivin
4、gatasteoftheprofoundpuzzlesthatphysicistsarestrugglingtosolve.1IntroductionTheStandardModelofparticlephysicsisoneofthegreatesttriumphsofphysics.Thistheoryisourbestattempttodescribealltheparticlesandalltheforcesofnature...exceptgravity.Itdoesagreatjobof?ttingexp
5、erimentswecandointhelab.Butphysicistsaredissatis?edwithit.Therearethreemainreasons.First,itleavesoutgravity:thatforceisdescribedbyEinstein’stheoryofgeneralrelativity,arXiv:0904.1556v2[hep-th]1May2010whichhasnotyetbeenreconciledwiththeStandardModel.Second,astron
6、omicalobservationssuggestthattheremaybeformsofmatternotcoveredbytheStandardModel—mostnotably,‘darkmatter’.Andthird,theStandardModeliscomplicatedandseeminglyarbitrary.Thisgoesagainstthecherishednotionthatthelawsofnature,whendeeplyunderstood,aresimpleandbeautiful
7、.Forthemoderntheoreticalphysicist,lookingbeyondtheStandardModelhasbeenanendeavorbothexcitingandfrustrating.Mostmodernattemptsarebasedonstringtheory.Therearealsootherinterestingapproaches,suchasloopquantumgravityandtheoriesbasedonnoncommutativegeometry.Butbackin
8、themid1970’s,beforeanyofthecurrentlypopularapproachesrosetoprominence,physicistspursuedaprogramcalled‘granduni?cation’.ThissoughttounifytheforcesandparticlesoftheStandardMod
