Gauge Symmetry in Fokker-Planck dynamics
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002naJ221v7911030/hp-pe:hviXraGaugesymmetryinFokker-Planckdynamics
M.deMontignya,b,F.C.Khannab,candA.E.Santanab,d
a
Facult´eSaint-Jean,UniversityofAlberta
8406-91Street,Edmonton,Alberta,CanadaT6C4G9b
TheoreticalPhysicsInstitute,UniversityofAlberta
Edmonton,Alberta,CanadaT6G2J1c
TRIUMF,4004,WesbrookMall
Vancouver,BritishColumbia,CanadaV6T2A3d
InstitutodeF´isica,UniversidadeFederaldaBahiaCampusdeOndina,Salvador,Bahia,Brazil40210-340
February1,2008
Abstract
UsingaGalileanmetricapproach,basedinanembeddingoftheEuclideanspaceintoa(4+1-Minkowskispace,weanalyzeagaugeinvariantLagrangianassociatedwithaRiemannianmanifoldR,withmetricg.Withaspecificchoiceofthegaugecondition,theEuler-LagrangeequationsarewrittencovariantlyinR,andthentheFokker-Planckequationisderived,suchthatthedriftandthediffusiontermsareobtainedfromg.Theanalysisiscarriedoutforboth,abelianandnonabeliansymmetries,andanexamplewiththesu(2symmetryispresented.
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1Introduction
InthispaperweshowthattheFokker-Planckequationcanbederivedviaagaugeinvarianttheory.ThebasicingredientinthederivationisGalileancovariance,whichhasbeenrecentlydevelopedindifferentperspectives,pro-vidingametric,andthus 