Quantum Mechanics of Fundamental Systems

From January 8-13,1990, distinguished physicists from many nations came to Chile to share with each other and with Latin American students exciting recent developments. The occasion was the third of a series of meetings on Quantum Mechanics of Fundamental Systems which are held every two years at the Centro de Estudios Cientificos de Santiago. This volume grew out from that gathering. The meeting was possible thanks to the generous support of the Tinker Foundation, the John D. and Catherine T. MacArthur Foundation, the International Centre for Theoretical Physics, the Ministere des AfIaires Etrangeres et Service Culturel et de Cooperation Scientifique et Technique de France, the Third World Academy of Sciences, and FONDECYT-Chile. The happy winds blowing over Chile at the time enhanced the joy provided by the beauty of the physics discussed. Claudio Teitelboim Jorge Zanelli Santiago, Chile vii Contents Chapter 1 Fractional Statistics in Quantum Mechanics Daniel P. Arovas 1. Introduction............................................. 1 2. Charge-Flux Composites. . . .. . . . .. . . . . . . . . .. . . . . . . . . .. . . . . 4 3. Dilute Anyon Gases . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 4. Fractional Statistics in the Quantized Hall Effect . . . . . . . . . . . . . 8 5. Many-Body Theory of the Anyon Gas... . .................. 16 6. Chern-Simons Field Theory and Fractional Statistics ......... 20 Appendix: Many Anyons in a Magnetic Field. . . . . . . . . . . . . . 23 . .

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This volume examines the latest advances emerging from the theoretical exploration into the quantum mechanical structure of our universe. It will be of interest to researchers dealing with strings, quantum fields, gauge theory, and quantum gravity.

Contenu
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 InvarianceBasic Requirements.- 4. Relativistic Description of Gauge-invariant Functions.- 5. The Koszul-Tate Resolution.- 6. The Exterior Derivative along the Gauge Orbits.- 7. BRST SymmetryMaster 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.