Quantum Mechanics of Fundamental Systems: Series of the Centro De Estudios Científicos

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.- References.- 3 Supersymmetry and Gauge Invariance in Stochastic Quantization.- 1. Introduction.- 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.- References.- 4 Covariant Superstrings.- 1. Introduction.- 2. The Minimal Covariant Action.- 3. Covariant Superstrings from the Light-Cone Gauge.- References.- 5 Constraints on the Baryogenesis Scale from Neutrino Masses.- 1. Introduction.- 2. Heavy Neutrino Decays.- 3. Conclusions.- References.- 6 The Antifield-BRST Formalism for Gauge Theories.- 1. Introduction.- 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.- References.- 7 Combinatorics of Mapping Class Groups and Matrix Integration.- 1. Introduction.- 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.- References.- 8 Field-theoretical Description of High-Tc Superconductors: Topological Excitations, GeneralizedStatistics, and Doping.- 1. Introduction.- 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.- References.- 9 Random Dynamics, Three Generations, and Skewness.- 1. Random Dynamics.- 2. Field Theory Glass.- 3. Skewness the Golden Principle.- References.- 10 Gauge Anomalies in Two Dimensions.- 1. Introduction.- 2. The Chiral Schwinger Model: The Effective Action.- 3. Solutions of the CSM.- 4. Non-Abelian Chiral Gauge Theory.- References.- 11 Some Topics in Topological Quantum Field Theories.- 1. Introduction.- 2. TQFTs and Stochastic Processes.- 3. Two-Dimensional Models.- 4. Topological Invariants.- References.