/

Methods of Quantization Lectures Held at the 39. Universitätswochen für Kern- und Teilchenphysik, Schladming, Austria

Latal Heimo Schweiger Wolfgang
Innbundet / 2001 / Engelsk

Product details

ISBN
9783540421009
Published
2001-07-17
Publisher
Springer-Verlag Berlin and Heidelberg GmbH & Co. KG
Height
235 mm
Width
155 mm
Age
Research, P, 06
Language
Product language
Engelsk
Format
Product format
Innbundet
Number of pages
11

Edited by
Latal Heimo
Schweiger Wolfgang

Methods of Quantization Lectures Held at the 39. Universitätswochen für Kern- und Teilchenphysik, Schladming, Austria

Latal Heimo Schweiger Wolfgang
Innbundet / 2001 / Engelsk
Latal Heimo Schweiger Wolfgang
Innbundet / 2001 / Engelsk
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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...
Read more
Most of our present understanding of the elementary building blocks of matter and the forces between them is based on the quantized version of the field theories which are locally symmetric under gauge transformations. The present set of lecture notes gives both a status report and a survey of recent advances for the most important quantization methods in the field theories for elementary particle physics. The first part of the book introduces light-cone quantization as an interesting alternative to the commonly used covariant perturbation theory and functional-integral methods. Next, a general formalism for quantizing systems with constraints, the projection-operator approach, is presented and structural aspects of the renormalization problem for gauge invariant field theories are discussed. Finally, the mathematics underlying the functional-integral quantization is reviewed. Suitable as a reference for researchers in the field, the book will prove particularly useful for lecturers and graduate students in search of additional reading beyond the standard texts on quantum field theory.
Read more
Includes supplementary material: sn.pub/extras
GPSR Compliance The European Union's (EU) General Product Safety Regulation (GPSR) is a set of rules that requires consumer products to be safe and our obligations to ensure this. If you have any concerns about our products you can contact us on ProductSafety@springernature.com. In case Publisher is established outside the EU, the EU authorized representative is: Springer Nature Customer Service Center GmbH Europaplatz 3 69115 Heidelberg, Germany ProductSafety@springernature.com
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Related products

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...
Read more
Most of our present understanding of the elementary building blocks of matter and the forces between them is based on the quantized version of the field theories which are locally symmetric under gauge transformations. The present set of lecture notes gives both a status report and a survey of recent advances for the most important quantization methods in the field theories for elementary particle physics. The first part of the book introduces light-cone quantization as an interesting alternative to the commonly used covariant perturbation theory and functional-integral methods. Next, a general formalism for quantizing systems with constraints, the projection-operator approach, is presented and structural aspects of the renormalization problem for gauge invariant field theories are discussed. Finally, the mathematics underlying the functional-integral quantization is reviewed. Suitable as a reference for researchers in the field, the book will prove particularly useful for lecturers and graduate students in search of additional reading beyond the standard texts on quantum field theory.
Read more
Includes supplementary material: sn.pub/extras
GPSR Compliance The European Union's (EU) General Product Safety Regulation (GPSR) is a set of rules that requires consumer products to be safe and our obligations to ensure this. If you have any concerns about our products you can contact us on ProductSafety@springernature.com. In case Publisher is established outside the EU, the EU authorized representative is: Springer Nature Customer Service Center GmbH Europaplatz 3 69115 Heidelberg, Germany ProductSafety@springernature.com
Read more

Product details

ISBN
9783540421009
Published
2001-07-17
Publisher
Springer-Verlag Berlin and Heidelberg GmbH & Co. KG
Height
235 mm
Width
155 mm
Age
Research, P, 06
Language
Product language
Engelsk
Format
Product format
Innbundet
Number of pages
11

Edited by
Latal Heimo
Schweiger Wolfgang

Related products