Methods of Quantization

Lectures Held at the 39. Universitätswochen für Kern- und Teilchenphysik, Schladming, Austria
Softcover Nachdruck of the original 1. Auflage 2001
ISBN: 978-3-662-14336-0
Verlag: Springer

Buch, Englisch, Band 572, 228 Seiten, Paperback, Format (B × H): 155 mm x 235 mm, Gewicht: 376 g

Reihe: Lecture Notes in Physics

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. 53 VIII Contents Light-ConeQuantization:FoundationsandApplications ThomasHeinzl.

Zielgruppe

Research

Autoren/Hrsg.

Schweiger, Wolfgang

Latal, Heimo

Fachgebiete

• Naturwissenschaften Physik Quantenphysik Teilchenphysik
• Naturwissenschaften Physik Physik Allgemein Theoretische Physik, Mathematische Physik, Computerphysik

Inhaltsverzeichnis

Forms of Relativistic Dynamics.- Light-Cone Quantization: Foundations and Applications.- Quantization of Constrained Systems.- Algebraic Methods of Renormalization.- Functional Integrals for Quantum Theory.