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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."
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...
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