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1、FractionalStatisticsandChern-SimonsFieldTheoryin2+1DimensionsAvinashKhare∗InstituteofPhysics,SachivalayaMarg,Bhubaneswar751005,India.Email:khare@iopb.res.inAbstractThequestionofanyonsandfractionalstatisticsinfieldtheoriesin2+1dimensionswithChern-Simons(CS)termisdiscussedin
2、somedetail.Argu-mentsarespelledoutastowhyfractionalstatisticsisonlypossibleintwospacedimensions.ThisphenomenonismostnaturallydiscussedwithintheframeworkoffieldtheorieswithCSterm,henceasapreludetothisdiscus-sionIfirstdiscussthevariouspropertiesoftheCSterm.Inparticularitsrole
3、asagaugefieldmasstermisemphasized.InthepresenceoftheCSterm,anyonscanappearintwodifferentwaysi.e.eitherassolitonofthecorrespondingfieldtheoryorasafundamentalquantacarryingfractionalstatisticsandbothapproachesareelaboratedinsomedetail.arXiv:hep-th/9908027v14Aug1999*TobePublish
4、edinINSA(IndianNationalScienceAcademy)Book200011IntroductionManyofushavewonderedsometimeortheotherifonecanhavenontrivialscienceandtechnologyintwospacedimensions;buttheusualfeelingisthattwospacedimensionsdonotofferenoughscopeforit.Thisquestion,tothebestofmyknowledge,wasfirst
5、addressedin1884byE.A.Abbotinhissatir-icalnovelFlatland[1].Thefirstseriousbookonthistopicappearedin1907entitledAnepisodeofFlatland[2].InthisbookC.H.Hintonofferedglimpsesofthepossiblescienceandtechnologyintheflatland.AnicesummaryofthesetwobooksappearedasachapterentitledFlatlan
6、dinabookin1969editedbyMartinGardner[3].Inspiredbythissummary,in1979A.K.Dewd-ney[4]publishedabookwhichcontainsseverallawsofphysics,chemistry,astronomyandbiologyintheflatland.However,allthesepeoplemissedoneimportantcasewherephysicallawsaremuchmorecomplex,nontrivialandhencein
7、terestingintheflatlandthaninourthreedimensionalworld.Iamreferringheretothecaseofquantumstatistics.Inlasttwodecadesithasbeenrealizedthatwhereasinthreeandhigherspacedimensionsallparti-clesmusteitherbebosonsorfermions(i.e.theymusthavespinofnh¯or(2n+1)¯h/2withn=0,1,2,...andmus
8、tobeyBose-EinsteinorFermi-Diracstatisticsrespectively),intwospacedimensionstheparticlescanhavean
