Symmetries in Constrainde Canonical Systems（影印版）

　　A dynamical system described by a singular Lagrangian is subject to some in- herent phase space constraints and is called a constrained canonical system （or con- strained Hamiltonian system）. Gauge field theories （for example， QED， QFD， QCD， Supergravity， Superstring） belong to this category. These theories now dominate particle physics. The theory of a constrained canonical system can also be applied to the theories of condensed matter and some other research area （for ex- ample， the quantum field theories of anyons）. The theories of a constrained canon- ical system play a fundamental role in modern field theories. The quantization of a constrained canonical system with a singular Lagrangian remains one of the key problems of quantum field theory and is being intensively discussed in the litera- ture. Symmetry is now a fundamental concept in modern physics. As it is well known， the discussion of symmetry properties of a system is usually based on the examination of the Lagranigan in configuration space. In quantum theory， the phase-space path integral is more fundamental than the configuration-space path integral， the latterprovides for a Hamiltonian quadratic in canonical momenta， whereas the former can be applied to an arbitrary Hamiltonian. Thus， the phase- space form of the path integral is a necessary precursor to the configuration-space form of the path integral. Therefore， the investigation of symmetry properties of a system in phase space has a basic sense in quantum theories， which can be applied to more general cases.

暂缺《Symmetries in Constrainde Canonical Systems（影印版）》作者简介

ChapterIConstrainedCanonicalSystemsandTheirQuantization
1.1TheCanonicalFormalismforaSystemwithaSingularLagrangian
1.2First-ClassConstraintsandSecond-ClassConstraints
13DiracBrackets
14TheFirst-ClassConstraintsandGaugeTransformation
I5GaugeFixing
16FieldTheorywithCanonicalConstraints
17DiracCanonicalQuantization
18ThePathIntegralQuantization
19PathIntegralQuantizationofConstrainedcanonicalSystems
110QuantizationoftheYang-MillsFields
111TheBFVPathIntegralQuantization
112BFVQuantizationofScalarQEDwithChern-SimonsTerms
ChapterIIClassicalCanonicalSymmetries
2.1GlobalCanonicalSymmetryforaSystemwithaSingularLagrangian
2.2CanonicalNoetherIdentitiesinPhaseSpace
2.3NonrelativisticChargeParticlesinanElectromagneticField
2.4TheGeneratorsofGaugeTransformation
2.5Poincare-CartanIntegralInvariantforaConstrainedCanonicalSystem
2.6Poincare-CartanIntegralInvariantandCanonicalEquationsforaConstrainedCanonicalSystem
2.7Dirac'sConjecture
2.8NoetherTheoreminCanonicalFormalismforaSingularLagrangianwithSubsidiaryConstraints
2.9TheInverseTheoremoftheCanonicalNoetherTheorem
2.10Poincare-CartanIntegralInvariantforaSingularConstrainedSystem
2.11NoetherTheoreminCanonicalFormalismforFieldTheories
2.12NoetherIdentitiesinCanonicalFormalismforFieldTheories
2.13TheElectromagneticFieldCoupledtoaChargeBosonField
2.14Yang-MillsFieldsCoupledtoaScalarField
2.15TheGeneratorsofGaugeTransformationforFieldTheories
ChapterIIISynunetriesinthePathIntegral
3.1TranslationInvarianceandQuantalCanonicalEquations
3.2CanonicalWardIdentitiesforLocalTransformation
3.3TheGaugeInvarianeeMassiveVectorField
3.4Non-AbelianGaugeFieldsCoupledtoSpinorField
3.5CanonicalWardIdentitiesforNon-LocalTransformation
3.6CanonicalWardIdentitiesforGlobalTransformation
3.7GlobalCanonicalSymmetriesandConservationLawsattheQuantumLevel
3.8ASystemofInteractingNucleonsandPions
3.9TheGeneratingFunctionalforaSystemofInteractingPhotons,ElectronsandPhonons
3.10CanonicalWardIdentitiesandQuantalConservedChargesforPhotonElectron-PhononInteraction
3.11QuantalGlobalCanonicalSymmetriesinYang-MillsFields
3.12Chem-SimonsTheories
3.13NonlinearSigmaModelwithaHopfandChern-SimonsTerms
3.14QuantalConservedChargeinNon-AbelianChern-SimonsTheories'
3.15SymmetriesinConfignration-SpacePathIntegral
ChapterIVCanonicalSynunetriesinaSystemwithaSingularHigher-OrderLagrangian
4.1TheorieswithHigher-OrderDerivatives
4.2CanonicalFormalismforaSystemwithaSingularHigher-OrderLagrangian
4.3ClassicalGlobalCanonicalSymmetries
4.4ClassicalLocalCanonicalSymmetries
4.5GeneralizedPoincare-CartanIntegralInvariant
4.6Dirac'sConjectureforaSystemwithaSingularHigher-OrderLagrangian
4.7GaugeGeneratorsforaSingularHigh-OrderLagrangian
4.8GeneralizedCanonicalNoetherTheoreminFieldTheories
4.9GeneralizedCanonicalNoetherIdentitiesinFieldTheories
4.10GeneralizedPoineare-CartanIntegralInvariantinFieldTheories
4.11ConstructionoftheGaugeGeneratorsforaSingularHigher-OrderLagrangianinFieldTheories
4.12GeneralizedCanonicalWardIdentities
4.13QuantalConservedLawsinTheorieswithHigher-OrderDerivatives
4.14QuantalSymmetriesinConfigurationSpaceforaGauge-InvariantSystem
4.15GaugeInvarianceMassiveVectorFieldwithHigher-OrderDerivatives
4.16Yang-MillsTheorieswithHigher-OrderDerivatives
4.17GeneralizedQCD
4.18Non-AbelianHigher-DerivativeChem-SimonsTheories
Index