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1、HomeSearchCollectionsJournalsAboutContactusMyIOPscienceFermioniccoherentstatesThisarticlehasbeendownloadedfromIOPscience.Pleasescrolldowntoseethefulltextarticle.2012J.Phys.A:Math.Theor.45244005(http://iopscience.iop.org/1751-8121/45/24/244005)Viewthetableofconte
2、ntsforthisissue,orgotothejournalhomepageformoreDownloaddetails:IPAddress:210.77.15.90Thearticlewasdownloadedon02/01/2013at04:05Pleasenotethattermsandconditionsapply.IOPPUBLISHINGJOURNALOFPHYSICSA:MATHEMATICALANDTHEORETICALJ.Phys.A:Math.Theor.45(2012)244005(27pp)
3、doi:10.1088/1751-8113/45/24/244005REVIEWFermioniccoherentstatesMoniqueCombescure1andDidierRobert21LaboratoiredePhysiqueTheorique,CNRS-UMR8627IPNL,B´atimentPaulDirac,4rueEnricoFermi,UniversiteLyon-1,F-69622VilleurbanneCedex,France´2DepartementdeMath´ematiques,Lab
4、oratoireJeanLeray,CNRS-UMR6629,´UniversitedeNantes,2ruedelaHoussini´ere,F-44322NantesCedex03,France`E-mail:monique.combescure@ipnl.in2p3.frandDidier.Robert@math.univ-nantes.frReceived19October2011,infinalform27February2012Published30May2012Onlineatstacks.iop.org/
5、JPhysA/45/244005AbstractTheaimofthispaperistogiveaself-containedandunifiedpresentationofafermioniccoherentstatetheorywiththenecessarymathematicaldetails,discussingtheirdefinition,propertiesandsomeapplications.AfterdefiningGrassmannalgebras,itispossibletogetaclassic
6、alanalogforthefermionicdegreesoffreedominaquantumsystem.FollowingthebasicworkofBerezin(1966TheMethodofSecondQuantization(NewYork:Academic);1987IntroductiontoSuperanalysis(Dordrecht:ReidelPublishingCompany)),weshowthatwecancomputewithGrassmannnumbersaswedowithcom
7、plexnumbers:derivation,integration,Fouriertransform.Afterthatweshowthatwehavequantizationformulasforfermionicobservables.Inparticular,thereexistsaMoyalproductformula.Asanapplication,weconsiderexplicitcomputationsforpropagatorswithquadraticHamiltoniansinannihilat
8、ionandcreationoperators.WeproveaMehlerformulaforthepropagatorandMehligWilkinson-typeformulasforthecovariantandcontravariantsymbolsofmetaplectictransformationsforfermi
