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 ontheKaluza-Kleinprogramforsupergravity(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. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1 Introduction. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 2 ThePoincar´eGroup. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 3 FormsofRelativisticDynamics. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 3. 1 ComparisonofInstantForm, FrontForm, andPointForm. . . 6 4 Light-FrontDynamics. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 4. 1 RelativeMomentum, InvariantMass. . . . . . . . . . . . . . . . . . . . . . 9 4. 2 TheBoxDiagram. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14 5 Poincar´eGeneratorsinFieldTheory. . . . . . . . . . . . . . . . . . . . . . . . . . . 19 5. 1 FermionsInteractingwithaScalarField. . . . . . . . . . . . . . . . . . . 20 5. 2 InstantForm. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20 5. 3 FrontForm(LF). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21 5. 4 InteractingandNon-interactingGeneratorsonanInstant andontheLightFront. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22 6 Light-FrontPerturbationTheory. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23 6. 1 ConnectionofCovariantAmplitudes toLight-FrontAmplitudes. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24 6. 2 Regularization. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26 6. 3 MinusRegularization. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26 7 TriangleDiagraminYukawaTheory. . . . . . . . . . . . . . . . . . . . . . . . . . . 27 7. 1 CovariantCalculation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28 7. 2 ConstructionoftheCurrentinLFD. . . . . . . . . . . . . . . . . . . . . . . 30 7. 3 NumericalResults. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37 3 8 FourVariationsonaThemein? Theory. . . . . . . . . . . . . . . . . . . . . . 37 8. 1 CovariantCalculation. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39 8. 2 Instant-FormCalculation. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42 8. 3 CalculationinLight-FrontCoordinates. . . . . . . . . . . . . . . . . . . . 47 8. 4 Front-FormCalculation. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49 9 DimensionalRegularization:BasicFormulae. . . . . . . . . . . . . . . . . . . . 51 10 Four-DimensionalIntegration. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52 11 SomeUsefulIntegrals. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53 References. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . | Methods of | Methods of Quantization by Heimo Latal, Paperback | Indigo Chapters