Quantum Mechanics of Fundamental Systems

Inhaltsverzeichnis

• 1 Fractional Statistics in Quantum Mechanics.
• 1. Introduction.
• 2. Charge-Flux Composites.
• 3. Dilute Anyon Gases.
• 4. Fractional Statistics in the Quantized Hall Effect.
• 5. Many-Body Theory of the Anyon Gas.
• 6. Chern-Simons Field Theory and Fractional Statistics.
• Appendix: Many Anyons in a Magnetic Field.
• References.
• 2 Microscopic and Macroscopic Loops in Nonperturbative Two-Dimensional Gravity.
• 3 Supersymmetry and Gauge Invariance in Stochastic Quantization.
• 2. Langevin Equations for Theories with a Yang-Mills Symmetry.
• 3. The Partition function.
• 4. The Case of Diffeomorphism Invariance.
• 5. The Case of First-Order Systems.
• 4 Covariant Superstrings.
• 2. The Minimal Covariant Action.
• 3. Covariant Superstrings from the Light-Cone Gauge.
• 5 Constraints on the Baryogenesis Scale from Neutrino Masses.
• 2. Heavy Neutrino Decays.
• 3. Conclusions.
• 6 The Antifield-BRST Formalism for Gauge Theories.
• 2. Structure of the Gauge Symmetries.
• 3. Gauge Invariance and BRST Invariance—Basic Requirements.
• 4. Relativistic Description of Gauge-invariant Functions.
• 5. The Koszul-Tate Resolution.
• 6. The Exterior Derivative along the Gauge Orbits.
• 7. BRST Symmetry—Master Equation.
• 8. Path Integral.
• 9. Examples.
• Appendix: Abelianization of the Gauge Transformations.
• 7 Combinatorics of Mapping Class Groups and Matrix Integration.
• 2. Matrix Integration Revisited.
• 3. Harmonic Oscillator and Fermions.
• 4. The Virtual Euler Characteristic of the Mapping Class Group.
• 5. Direct Method.
• 6. Concluding Remarks.
• 8 Field-theoretical Description of High-Tc Superconductors: Topological Excitations, GeneralizedStatistics, and Doping.
• 2. The Continuum Model for High-Tc Superconductors.
• 3. Quantization of Topological Excitations in the Continuum Models for the New Superconductors.
• 4. Generalized Statistics and Superconductivity.
• 5. Introduction of Dopants: A Possible Mechanism of Superconductivity.
• 9 Random Dynamics, Three Generations, and Skewness.
• 1. Random Dynamics.
• 2. Field Theory Glass.
• 3. Skewness the Golden Principle.
• 10 Gauge Anomalies in Two Dimensions.
• 2. The Chiral Schwinger Model: The Effective Action.
• 3. Solutions of the CSM.
• 4. Non-Abelian Chiral Gauge Theory.
• 11 Some Topics in Topological Quantum Field Theories.
• 2. TQFTs and Stochastic Processes.
• 3. Two-Dimensional Models.
• 4. Topological Invariants.