Particles and Fields

Inhaltsverzeichnis

• 1 Recent Developments in Affine Toda Quantum Field Theory.
• 1 Introduction.
• 2 Classical Integrability and Classical Data.
• 3 Aspects of the Quantum Field Theory.
• 4 Dual Pairs.
• 5 A Word on Solitons.
• 6 Other Matters.
• 7 References.
• 2 A Class of Fermi Liquids.
• 2 Four-Legged Diagrams.
• 3 A Single-Slice Fermionic Cluster Expansion.
• 4 References.
• 3 Quantum Groups from Path Integrals.
• 1 Classical Field Theory.
• 2 Categories, Finite Groups, and Covering Spaces.
• 3 Generalized Path Integrals.
• 4 The Quantum Group.
• 5 References.
• 4 Half Transfer Matrices in Solvable Lattice Models.
• 1 The Six-Vertex Model.
• 2 The Antiferromagnetic Regime.
• 3 Corner Transfer Matrix.
• 4 Half Transfer Matrix.
• 5 Commutation Relations.
• 6 Correlation Functions.
• 7 Two-Point Functions.
• 8 Discussion.
• 9 References.
• 5 Matrix Models as Integrable Systems.
• 2 The Basic Example: Discrete 1-Matrix Model.
• 3 Generalized Kontsevich Model.
• 4 Kp/Toda ?-Function in Terms of Free Fermions.
• 5 ?-Function as a Group-Theoretical Quantity.
• 6 Conclusion.
• 6 Localization, Equivariant Cohomology, and Integration Formulas 211.
• 1 Symplectic Geometry.
• 2 Equivariant Cohomology.
• 3 Duistermaat-Heckman Integration Formula.
• 4 Degeneracies.
• 5 Equivariant Characteristic Classes.
• 6 Loop Space.
• 7 Example: Atiyah-Singer Index Theorem.
• 8 Duistermaat-Heckman in Loop Space.
• 9 General Integrable Models.
• 10 Mathai-Quillen Formalism.
• 11 Short Review of Morse Theory.
• 12 Equivariant Mathai-Quillen Formalism.
• 13 Equivariant Morse Theory.
• 14 Loop Space and Morse Theory.
• 15 Loop Space and Equivariant Morse Theory.
• 16 Poincaré Supersymmetry and Equivariant Cohomology..
• 17 References.
• 7 Systems of Calogero-Moser Type.
• 2 Classical NonrelativisticCalogero-Moser and Toda Systems.
• 3 Relativistic Versions at the Classical Level.
• 4 Quantum Calogero-Moser and Toda Systems.
• 5 Action-Angle Transforms.
• 6 Eigenfunction Transforms.
• 8 Discrete Gauge Theories.
• 1 Broken Symmetry Revisited.
• 2 Basics.
• 3 Algebraic Structure.
• 4 $${\overline D _2}$$ Gauge Theory.
• 5 Concluding Remarks and Outlook.
• 6 References.
• 9 Quantum Hall Fluids as W1+? Minimal Models.
• 2 Dynamical Symmetry and Kinematics of Incompressible Fluids.
• 3 Existing Theories of Edge Excitations and Experiments.
• 4 W1+? Minimal Models.
• 5 Further Developments.
• 10 On the Spectral Theory of Quantum Vertex Operators 469 Pavel I. Etingof.
• 1 Basic Definitions.
• 2 Spectral Properties of Vertex Operators.
• 3 The Semi-Infinite Tensor Product Construction.
• 4 Computation of the Leading Eigenvalue and Eigenvector.