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1、GaugeprocedurewithgaugefieldsofvariousranksDouglasSingleton∗CentreofGravitationandFundamentalMetrology,VNIIMS,3-1M.UlyanovoySt.,Moscow119313,Russia;PhysicsDept.,CSUFresno,2345EastSanRamonAve.M/S37Fresno,CA93740-8031AkiraKato†PhysicsDept.,CSUFresno,2345EastSanRamonAve.M/S3
2、7Fresno,CA93740-8031A.Yoshida‡ScienceDept.,SaintAnne’sBelfieldSchool,Charlottesville,VA22903(Dated:February1,2008)Thestandardprocedureformakingaglobalphasesymmetrylocalinvolvestheintroductionofarank1,vectorfieldinthedefinitionofthecovariantderivative.Hereitisshownthatitispo
3、ssibletogaugeaphasesymmetryusingfieldsofvariousranks.Incontrasttootherformulationsofhigherrankgaugefieldswebeginwiththecouplingofthegaugefieldtosomematterfield,andthenderivethegaugeinvariant,fieldstrengthtensor.Someofthesegaugetheoriesaresimilartogeneralrelativityinthattheirc
4、ovariantderivativesinvolvederivativesoftherankngaugefieldratherthanjustthegaugefield.ForgeneralrelativitythecovariantderivativeinvolvestheChristoffelsymbolswhicharewrittenintermsofderivativesofthemetrictensor.Many(butnotall)oftheLagrangiansthatwefindforthesehigherrankgaugeth
5、eoriesleadtononrenormalizablequantumtheorieswhichisalsosimilartogeneralrelativity.PACSnumbers:03.50.-z,11.15.-qI.STANDARDGAUGEPROCEDUREWITHARANK1FIELDTheconceptofsymmetries,andtheprocessofturningglobalsymmetriesintolocalones(i.e.gaugingthesymmetry)areimportantfeaturesofm
6、odernfieldtheories.AnexampleisMaxwell’stheory,whichcanbederivedfromthegaugeprincipleappliedtoanAbelianU(1)symmetryofsomematterfield.Inthissectionwesummarizethestandardgaugeprocedure.Forourmatterfieldwewilluseacomplexscalarmatterfield,ϕ,throughoutthepaper.Thesameprocedureappl
7、iesstartingwithothertypesofmatterfield(e.g.aspinorfield).TheLagrangedensityforthematterfield,ϕ,is∗µLscalar=(∂µϕ)(∂ϕ)+...(1)Theellipsesleaveoffmass,m2ϕ∗ϕ,andself-interactionterms,λ(ϕ∗ϕ)2,thatdon’tinvolvederivativesofϕ.ThisarXiv:hep-th/0408031v27Oct2004Lagrangedensitysatisfiest
8、heglobalphasesymmetryϕ(x)→e−igΛϕ(x),ϕ∗(x)→eigΛϕ∗(x),(2)wheregisthecouplingandΛisaconstant.Thisphasesymm
