Quantum field theories based on noncommutative space-time (NCQFT) have been extensively studied recently. However no NCQFT model, which can uniquely describe the strong and electroweak interactions, has been constructed. This prevents consistent and system
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aStrongandElectroweakInteractions,andTheirUni cationwithNoncommutativeSpace-TimeXiao-GangHeInstituteofTheoreticalPhysics,AcademiaSinica,Beijing100080andDepartmentofPhysics,NationalTaiwanUniversity,Taipei10764AbstractQuantum eldtheoriesbasedonnoncommutativespace-time(NCQFT)havebeenextensivelystudiedrecently.HowevernoNCQFTmodel,whichcanuniquelydescribethestrongandelectroweakinteractions,hasbeencon-structed.Thispreventsconsistentandsystematicstudyofnoncommutativespace-time.InthisworkweconstructaNCQFTmodelbasedonthetrini- cationgaugegroupSU(3)C×SU(3)L×SU(3)R.Auniquefeatureofthismodel,thatallmatter elds(fermionsandHiggses)areassignedto(anti-)fundamentalrepresentationsofthefactorSU(3)groups,allowsustocon-structaNCQFTmodelforstrongandelectroweakinteractionsandtheiruni-
cationwithoutambiguities.Thismodelprovidesanexamplewhichallows
consistentandsystematicstudyofnoncommutativespace-timephenomenol-
ogy.WealsocommentonsomerelatedissuesregardingextensionstoE6and
U(3)C×U(3)L×U(3)Rmodels.
PACSnumbers:22.20-z,11.15-q,12.10,12.60-i
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