Methods of Quantization

ofquantum?eldtheories,werehighlightedinthelecturesofBernardBakker andThomasHeinzl. Oneoftheopenproblemsoflight-conequantizationis theissueofspontaneoussymmetrybreaking. Thiscanbetracedbacktozero modeswhich,ingeneral,aresubjecttocomplicatedconstraintequations. A generalformalismforthequantizationofphysicalsystemswithconstraints waspresentedbyJohnKlauder. Theperturbativede?nitionofquantum?eld theoriesisingenerala?ictedbysingularitieswhichareovercomebyare- larizationandrenormalizationprocedure. Structuralaspectsoftherenormal- VI Preface izationprobleminthecaseofgaugeinvariant?eldtheorieswerediscussed inthelectureofKlausSibold. Areviewofthemathematicsunderlyingthe functional-integralquantizationwasgivenbyLudwigStreit. Apartfromthetopicsincludedinthisvolumetherewerealsolectures ontheKaluzäKleinprogramforsupergravity(P. vanNieuwenhuizen),on dynamicalr-matricesandquantization(A. Alekseev),andonthequantum Liouvillemodelasaninstructiveexampleofquantumintegrablemodels(L. Faddeev). Inaddition,theschoolwascomplementedbymanyexcellents- inars. Thelistofseminarspeakersandthetopicsaddressedbythemcanbe foundattheendofthisvolume. Theinterestedreaderisrequestedtocontact thespeakersdirectlyfordetailedinformationorpertinentmaterial. Finally,wewouldliketoexpressourgratitudetothelecturersforalltheir e?ortsandtothemainsponsorsoftheschool,theAustrianMinistryofE- cation,Science,andCultureandtheGovernmentofStyria,forprovidingg- eroussupport. Wealsoappreciatethevaluableorganizationalandtechnical assistanceofthetownofSchladming,theSteyr-Daimler-PuchFahrzeugte- nik, Ricoh Austria, Styria Online, and the Hornig company. Furthermore, wethankoursecretaries,S. FuchsandE. Monschein,anumberofgra- atestudentsfromourinstitute,and,lastbutnotleast,ourcolleaguesfrom theorganizingcommitteefortheirassistanceinpreparingandrunningthe school. Graz, HeimoLatal March2001 WolfgangSchweiger Contents FormsofRelativisticDynamics BernardL. G. Bakker. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .