Language: English
ISBN/ISSN: 7030095820
Published on: 2002-01
Hardcover
Contents
Chapter I Constrained Canonical Systems and Their Quantization
1.1 The Canonical Formalism for a System with a Singular Lagrangian
1.2 First-Class Constraints and Second-Class Constraints
1 3 Dirac Brackets
1 4 The First-Class Constraints and Gauge Transformation
I 5 Gauge Fixing
1 6 Field Theory with Canonical Constraints
1 7 Dirac Canonical Quantization
1 8 The Path Integral Quantization
1 9 Path Integral Quantization of Constrained canonical Systems
1 10 Quantization of the Yang-Mills Fields
1 11 The BFV Path Integral Quantization
1 12 BFV Quantization of Scalar QED with Chern-Simons Terms
Chapter II Classical Canonical Symmetries
2.1 Global Canonical Symmetry for a System with a Singular Lagrangian
2.2 Canonical Noether Identities in Phase Space
2.3 Nonrelativistic Charge Particles in an Electromagnetic Field
2.4 The Generators of Gauge Transformation
2.5 Poincare-Cartan Integral Invariant for a Constrained Canonical System
2.6 Poincare-Cartan Integral Invariant and Canonical Equations for a Constrained Canonical System
2.7 Dirac's Conjecture
2.8 Noether Theorem in Canonical Formalism for a Singular Lagrangian with Subsidiary Constraints
2.9 The Inverse Theorem of the Canonical Noether Theorem
2.10 Poincare-Cartan Integral Invariant for a Singular Constrained System
2.11 Noether Theorem in Canonical Formalism for Field Theories
2.12 Noether Identities in Canonical Formalism for Field Theories
2.13 The Electromagnetic Field Coupled to a Charge Boson Field
2.14 Yang-Mills Fields Coupled to a Scalar Field
2.15 The Generators of Gauge Transformation for Field Theories
Chapter III Synunetries in the Path Integral
3.1 Translation Invariance and Quantal Canonical Equations
3.2 Canonical Ward Identities for Local Transformation
3.3 The Gauge Invarianee Massive Vector Field
3.4 Non-Abelian Gauge Fields Coupled to Spinor Field
3.5 Canonical Ward Identities for Non-Local Transformation
3.6 Canonical Ward Identities for Global Transformation
3.7 Global Canonical Symmetries and Conservation Laws at the Quantum Level
3.8 A System of Interacting Nucleons and Pions
3.9 The Generating Functional for a System of Interacting Photons, Electrons and Phonons
3.10 Canonical Ward Identities and Quantal Conserved Charges for PhotonElectron-Phonon Interaction
3.11 Quantal Global Canonical Symmetries in Yang-Mills Fields
3.12 Chem-Simons Theories
3.13 Nonlinear Sigma Model with a Hopf and Chern-Simons Terms
3.14 Quantal Conserved Charge in Non-Abelian Chern-Simons Theories'
3.15 Symmetries in Confignration-Space Path Integral
Chapter IV Canonical Synunetries in a System with a Singular Higher-Order Lagrangian
4.1 Theories with Higher-Order Derivatives
4.2 Canonical Formalism for a System with a Singular Higher-Order Lagrangian
4.3 Classical Global Canonical Symmetries
4.4 Classical Local Canonical Symmetries
4.5 Generalized Poincare-Cartan Integral Invariant
4.6 Dirac' s Conjecture for a System with a Singular Higher-Order Lagrangian
4.7 Gauge Generators for a Singular High-Order Lagrangian
4.8 Generalized Canonical Noether Theorem in Field Theories
4.9 Generalized Canonical Noether Identities in Field Theories
4.10 Generalized Poineare-Cartan Integral Invariant in Field Theories
4.11 Construction of the Gauge Generators for a Singular Higher-Order Lagrangian in Field Theories
4.12 Generalized Canonical Ward Identities
4.13 Quantal Conserved Laws in Theories with Higher-Order Derivatives
4.14 Quantal Symmetries in Configuration Space for a Gauge-Invariant System
4.15 Gauge Invariance Massive Vector Field with Higher-Order Derivatives
4.16 Yang-Mills Theories with Higher-Order Derivatives
4.17 Generalized QCD
4.18 Non-Abelian Higher-Derivative Chem-Simons Theories
Index
