Il capitano generale lagrimo per allegrezza e nomino quel capo: Deseado, perehe l'avevamo gia gran tempo desiderato. Antonio Pigafetta Il Primo Viaggo in torno al Mondo I would like to take some poetic license in introducing this volume in a way that seems appropriate for a country, like Chile, that Iooks to the ocean. I believe it was Heisenberg who compared different times in physics with sailing a ship. He said that most of the time we keep our ships in port, or in the protection of a bay. But on a few occasions we go into the open sea, and those occasions are really the great times in theoretical physics, when everything can change. It does not seem totally unwarranted to hope that we are now entering one of those times. In that spirit, I would like to mention a wonderful book, which in English would be called something like Chile, Or a Crazy Geography.

Il capitano generale lagrimo per allegrezza e nomino quel capo: Deseado, perehe l'avevamo gia gran tempo desiderato. Antonio Pigafetta Il Primo Viaggo in torno al Mondo I would like to take some poetic license in introducing this volume in a way that seems appropriate for a country, like Chile, that Iooks to the ocean. I believe it was Heisenberg who compared different times in physics with sailing a ship. He said that most of the time we keep our ships in port, or in the protection of a bay. But on a few occasions we go into the open sea, and those occasions are really the great times in theoretical physics, when everything can change. It does not seem totally unwarranted to hope that we are now entering one of those times. In that spirit, I would like to mention a wonderful book, which in English would be called something like Chile, Or a Crazy Geography.

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 . .

This volume is based on a meeting on Quantum Mechanics of Fundamental Systems, held December 17-20 of 1987, at the Centro de Estudios Cientificos de Santiago (CECS). The meeting was intended to review new developments in the field defined by its purposely vague title. We were especially interested in communicating important advances in a broad perspective and in a self-contained manner to a wide colleague- ship, and in particular to Latin American physicists. Whatever success we may have achieved in that direction would cer- tainly not have been possible without the help and generosity of many people. For their kind support we thank the Tinker Foundation, the Inter- national Centre for Theoretical Physics, the Ministere des Affaires Etrangeres et Service Culturel et de Cooperation Scientifique et Technique de France and the Centro Latinoamericano de Fisica. We are especially grateful to the Santiago College and to its principal, Rebeca Donoso, for allowing us to hold the meeting at that school when, at the last moment, we were deprived of the previously arranged meeting site. Last but not least we thank the participants for an extraordinary week and the CECS staff for performing, as usual, beyond any reasonable expectation.

This book is a systematic study of the classical and quantum theories of gauge systems. It starts with Dirac's analysis showing that gauge theories are constrained Hamiltonian systems. The classical foundations of BRST theory are then laid out with a review of the necessary concepts from homological algebra. Reducible gauge systems are discussed, and the relationship between BRST cohomology and gauge invariance is carefully explained. The authors then proceed to the canonical quantization of gauge systems, first without ghosts (reduced phase space quantization, Dirac method) and second in the BRST context (quantum BRST cohomology). The path integral is discussed next. The analysis covers indefinite metric systems, operator insertions, and Ward identities. The antifield formalism is also studied and its equivalence with canonical methods is derived. The examples of electromagnetism and abelian 2-form gauge fields are treated in detail.

The book gives a general and unified treatment of the subject in a self-contained manner. Exercises are provided at the end of each chapter, and pedagogical examples are covered in the text.