Thisvolumecontainsthewrittenversionsofinvitedlecturespresentedat the"39. InternationaleUniversitatswochenfur .. Kern-undTeilchenphysik"in Schladming, Austria, which took place from February 26th to March 4th, 2000. The title of the school was "Methods of Quantization". This is, of course,averybroad?eld,soonlysomeofthenewandinterestingdevel- mentscouldbecoveredwithinthescopeoftheschool. About75yearsagoSchrodingerpresentedhisfamouswaveequationand Heisenbergcameupwithhisalgebraicapproachtothequantum-theoretical treatmentofatoms. Aimingmainlyatanappropriatedescriptionofatomic systems, these original developments did not take into consideration E- stein'stheoryofspecialrelativity. WiththeworkofDirac,Heisenberg,and Pauliitsoonbecameobviousthatauni?edtreatmentofrelativisticandqu- tume?ectsisachievedbymeansoflocalquantum?eldtheory,i. e. anintrinsic many-particletheory. Mostofourpresentunderstandingoftheelementary buildingblocksofmatterandtheforcesbetweenthemisbasedonthequ- tizedversionof?eldtheorieswhicharelocallysymmetricundergaugetra- formations. Nowadays,theprevailingtoolsforquantum-?eldtheoreticalc- culationsarecovariantperturbationtheoryandfunctional-integralmethods. Beingnotmanifestlycovariant,theHamiltonianapproachtoquantum-?eld theorieslagssomewhatbehind,althoughitresemblesverymuchthefamiliar nonrelativisticquantummechanicsofpointparticles. Aparticularlyintere- ingHamiltonianformulationofquantum-?eldtheoriesisobtainedbyqu- tizingthe?eldsonhypersurfacesoftheMinkowsispacewhicharetangential tothelightcone. The"timeevolution"ofthesystemisthenconsideredin + "light-conetime"x =t+z/c. Theappealingfeaturesof"light-conequ- tization",whicharethereasonsfortherenewedinterestinthisformulation 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-odingerpresentedhisfamouswaveequationand Heisenbergcameupwithhisalgebraicapproachtothequantum-theoretical treatmentofatoms. Aimingmainlyatanappropriatedescriptionofatomic systems, these original developments did not take into consideration E- stein'stheoryofspecialrelativity. WiththeworkofDirac,Heisenberg,and Pauliitsoonbecameobviousthatauni?edtreatmentofrelativisticandqu- tume?ectsisachievedbymeansoflocalquantum?eldtheory,i. e. anintrinsic many-particletheory. Mostofourpresentunderstandingoftheelementary buildingblocksofmatterandtheforcesbetweenthemisbasedonthequ- tizedversionof?eldtheorieswhicharelocallysymmetricundergaugetra- formations. Nowadays,theprevailingtoolsforquantum-?eldtheoreticalc- culationsarecovariantperturbationtheoryandfunctional-integralmethods. Beingnotmanifestlycovariant,theHamiltonianapproachtoquantum-?eld theorieslagssomewhatbehind,althoughitresemblesverymuchthefamiliar nonrelativisticquantummechanicsofpointparticles. Aparticularlyintere- ingHamiltonianformulationofquantum-?eldtheoriesisobtainedbyqu- tizingthe? eldsonhypersurfacesoftheMinkowsispacewhicharetangential tothelightcone. The"timeevolution"ofthesystemisthenconsideredin + "light-conetime"x =t+z/c. Theappealingfeaturesof"light-conequ- tization",whicharethereasonsfortherenewedinterestinthisformulation 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...

In this volume seven leading theoreticians and experimenters review the origin of the asymmetry of matter and antimatter in the Big Bang, solar neutrinos, the physics of enormous densities and temperatures in stars and of immense magnetic fields around collapsed stars, strong electric fields in heavy ion collisions, and the extreme conditions in quark-gluon plasmas. The articles address nuclear and particle physicists, especially graduate students, but also astrophysicists and cosmologists, since they have to deal with events under the extreme physical conditions discussed here.

Thisvolumecontainsthewrittenversionsofinvitedlecturespresentedat the"39. InternationaleUniversitatswochenfur .. Kern-undTeilchenphysik"in Schladming, Austria, which took place from February 26th to March 4th, 2000. The title of the school was "Methods of Quantization". This is, of course,averybroad?eld,soonlysomeofthenewandinterestingdevel- mentscouldbecoveredwithinthescopeoftheschool. About75yearsagoSchrodingerpresentedhisfamouswaveequationand Heisenbergcameupwithhisalgebraicapproachtothequantum-theoretical treatmentofatoms. Aimingmainlyatanappropriatedescriptionofatomic systems, these original developments did not take into consideration E- stein'stheoryofspecialrelativity. WiththeworkofDirac,Heisenberg,and Pauliitsoonbecameobviousthatauni?edtreatmentofrelativisticandqu- tume?ectsisachievedbymeansoflocalquantum?eldtheory,i. e. anintrinsic many-particletheory. Mostofourpresentunderstandingoftheelementary buildingblocksofmatterandtheforcesbetweenthemisbasedonthequ- tizedversionof?eldtheorieswhicharelocallysymmetricundergaugetra- formations. Nowadays,theprevailingtoolsforquantum-?eldtheoreticalc- culationsarecovariantperturbationtheoryandfunctional-integralmethods. Beingnotmanifestlycovariant,theHamiltonianapproachtoquantum-?eld theorieslagssomewhatbehind,althoughitresemblesverymuchthefamiliar nonrelativisticquantummechanicsofpointparticles. Aparticularlyintere- ingHamiltonianformulationofquantum-?eldtheoriesisobtainedbyqu- tizingthe?eldsonhypersurfacesoftheMinkowsispacewhicharetangential tothelightcone. The"timeevolution"ofthesystemisthenconsideredin + "light-conetime"x =t+z/c. Theappealingfeaturesof"light-conequ- tization",whicharethereasonsfortherenewedinterestinthisformulation 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-odingerpresentedhisfamouswaveequationand Heisenbergcameupwithhisalgebraicapproachtothequantum-theoretical treatmentofatoms. Aimingmainlyatanappropriatedescriptionofatomic systems, these original developments did not take into consideration E- stein'stheoryofspecialrelativity. WiththeworkofDirac,Heisenberg,and Pauliitsoonbecameobviousthatauni?edtreatmentofrelativisticandqu- tume?ectsisachievedbymeansoflocalquantum?eldtheory,i. e. anintrinsic many-particletheory. Mostofourpresentunderstandingoftheelementary buildingblocksofmatterandtheforcesbetweenthemisbasedonthequ- tizedversionof?eldtheorieswhicharelocallysymmetricundergaugetra- formations. Nowadays,theprevailingtoolsforquantum-?eldtheoreticalc- culationsarecovariantperturbationtheoryandfunctional-integralmethods. Beingnotmanifestlycovariant,theHamiltonianapproachtoquantum-?eld theorieslagssomewhatbehind,althoughitresemblesverymuchthefamiliar nonrelativisticquantummechanicsofpointparticles. Aparticularlyintere- ingHamiltonianformulationofquantum-?eldtheoriesisobtainedbyqu- tizingthe? eldsonhypersurfacesoftheMinkowsispacewhicharetangential tothelightcone. The"timeevolution"ofthesystemisthenconsideredin + "light-conetime"x =t+z/c. Theappealingfeaturesof"light-conequ- tization",whicharethereasonsfortherenewedinterestinthisformulation 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...

th This volume contains the written versions of invited lectures presented at the 28 "Internationale Universitatswochen fUr Kernphysik" in Schladming, Austria in March 1989. The generous support of our sponsors, the Austrian Ministry of Science and Research, the Government of Styria, and others, made it again possible to invite expert lecturers. The courses were centered on elementary particle physics to be performed with large accelerators accessible in the immediate future, including some reports on the current situation. Thanks to the efforts of the speakers it was possible to obtain excellent surveys. After the School the lecture notes were revised and partially rewritten in TPC by the authors, whom we thank for their labour. Unfortunately the report on the situation at SLAC by M. Swartz could not be included. Thanks are also due to the publishers for their patience. Graz, Austria H. Latal December 1989 H. Mitter v Contents Phenomenology of and Beyond the Standard Electroweak Model By A. Bartl, H. Pietschmann, and H. Stremnitzer (With 6 Figures) 1 1. The Standard Model (H. Pietschmann) . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1. 1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1. 2 Defining the Standard Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1. 3 Testing the Standard Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 1. 4 Predictions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 1. 5 Open Questions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 1. 6 Hypotheses. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 1. 7 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 2. Beyond the Standard Model: Supersymmetry (A. Bartl) . . . . . . . . . . . . 9 2. 1 Supersymmetric Extension of the Standard Model . . . . . . . . . . . . 10 2. 2 Production and Decay of Supersymmetric Particles . . . . . . . . . . . 17 3. Beyond the Standard Model: Composite Models (H.

Twenty-five years of Schladming Winter School 1. The Start Twenty-five years ago P. Urban had the idea of organizing a winter school in the Austrian mountains. The very concept of a school was not new: to bring physicists together in an environment which differs totally from the daily world of institutes and laboratories, to contrast hard classroom work in lectures by distinguished speakers with a relaxed atmosphere, to provide opportunities for entering newly developing fields and exchanging ideas, all this had already resulted in a few summer schools in southern Europe and the US. The idea of combining physics with skiing rather than swimming was, however, new. After some sampling by a few younger members of Ur ban's group, Schladming was selected as an appropriate place. At that time skiing was not very much developed here; there were few lifts, but a road to Hochwurzen and a regular bus service opened at least one longer track. The first meeting took place in a classroom of the local school, w here some 40 participants were squeezed into benches designed for children. In the next year we moved into the dining hall of a small inn, which does not exist any more (an attempt to serve beer during the lectures was stopped by the orga nizing committee). Only in later years did we find a permanent home here in the Stadtsaal."