V Jorge Andre Swieca Summer School Field Theory and Particle Physics Campos do Jordão, Brazil f. 8-21 January 1989 Editors O.J.P. Éboli, 17. Gomes and A. Santoro World Scientific Singapore • New Jersey • London • Hong Kong Published by World Scientific Publishing Co. Pte. Ltd., P O Box 128, Fairer Road, Singapore 9128 USA office: 687 HatlweU Street, Teaneck, NJ G7666 UK office: 73 Lynton Mead, Totteridge, London N20 8DH Library of Congress Cataloging -in-Publication data is available. FIELD THEORY AND PARTICLE PHYSICS Copyright © 1990 by World Scientific Publishing Co. Pte. Ltd. All rights reserved. This book, or parts thereof, may not be reproduced in any form or by any means, electronic or mechanical, including photo- copying, recording or any information storage and retrieval system now known or to be invented, without written permission from the Publisher. ISBN 981-02-0057-9 Printed in Singapore by JBW Printer» & Binders Pte. Ltd. PREFACE The V Jorge André Swieca Summer School was held at Campos do Jordão, a small village near São Paulo, from January 8 to 21, 1989. This event provided a series of lectures and seminars delivered by invited speakers. These Proceedings contains the lectures notes of the topics covered during the school. The first part of the book collects the material devoted to quantum field the- ory. There were four courses on methods in Field Theory: H. 0. Girotti lectured on constrained dynamics, R. Jackiw on the Schrõdinger representation in Field Theory, S.-Y. Pi on the application of this representation to quantum fields in a Robertson- Walker spacetime, and L. Vinet on Berry Connections. There were three courses on Conformai Field Theory: I. Todorov focused on the problem of construction and classification of conformai field theories. Lattice models, two-dimensional 5 ma- trices and conformai field theory were looked from the unifying perspective of the .Yang-Baxter algebras in the lectures given by M. Karowski. Parasupersymmetric quantum mechanics was discussed in the lectures by L. Vinet. Besides those courses, there was an introdution to string field theory given by G. Horowitz. There were also three seminars: F. Schaposnik reported on recent applications of topological methods in field theory, P. Gêrbert gave a seminar on three dimensional gravity and V. Kurak talked on two dimensional parafermionic models. The second part of this proceedings is devoted to phenomenology. There were three courses on Particle Physics: Dan Green lectured on collider physics, E. Predrazzi on strong interactions and G. Cohen-Tanoudji on the use of strings in strong interactions. We would like to thank everybody who contributed for the success of the V Jorge Andre Swieca Summer School. Very special thanks are due to the lecturers who gave a very nice set of lectures and shared their knowledge and time with the participants. The School would not have been possible without the financial support from the following institutions: CLAF, SBF, FAPESP, ICTP (Trieste), FAPERJ, CNPq, CAPES, FINEP, IBM, FERMILAB and the University of Sio Paulo. O.J.P. Éboli M. Gomes A. Santoro Lecturers and Topics G. Cohen-Tannoudji (Saclay) QCD and Hadronic Strings H . 0. Girotti (UFRGS) Classical and Quantum Dynamics of Constrained Systems D. Green (Fermilab) pp Collider Physics G. Horowitz (Santa Barbara) Introduction to String Field Theory R. Jackiw (MIT) Analysis on Infinite Dimensional Manifolds Schrõdinger Representation for Quantized Fields M. Karowski (ETH) Yang-Baxter Algebra - Integrable Systems - Conformai Quantum Field Theories S.-Young. Pi (BÜ) Quantum Field Theory in Flat Robertson-Walker Space-Time: Functional Schrõdinger Picture E. Predazzi (Turim) Strong Interaction Phenomenology I. Todorov (Sofia) Rational Conformai Theories Involving a U(l) Current Algebra L. Vinet (Montreal) Dynamical Parasupersymmetries in Quantum Mechanics- Berry Connections Seminar speakers P. S. Gerbert (MIT) Gravity in 2 + 1 Dimensions V. Kurak (IFUSP) Parafcrmioníc Conformai Field Theory F. Schaposnick (La Plata) Topological Field Theories and Two Dimensional Instantons Vtt Participants AbdaJla, E. IFUSP Abdalla, M.C.B. IFT UNESP Almeida, C.A.S. CBPF Almeida, L.D. IFT UNESP Amaral, R.L.P.G. PUCRJ Alves, M.S. ÜFRJ Bazeia Filho, D. UFPB Bedaque, P.S.F. IFUSP Belletato, P. PUCRJ Biancolin, M.M IFUSP Botelho, L.C. UFPA Bouzas, A.O. La Plata Brunelli, J.C. IFUSP Brunetto, S.Q. UNICAMP Brunint, S.A. IFUSP Caldas, P.S.S- IFUSP Carvalho, H.F.de UFRJ Carvalho, L.de C. CBPF Constantinidis, C.P. IFQSC Covolan, R.J.M. UNICAMP Demarco, G.L CAB Dias, S.A. CBPF Ducatti, M.B.G. UFRGS Dutra, A.de S. CBPF Evangelista, L.R. FUEM Ferreira, L.A. IFT UNESP Figueiredo, B.D.B CBPF Foster, A. UFRGS Gerbert, P.S. MIT Gones, J.F. IFT UNESP Gonade, J.R. IFÜSP Hasiran, N.M. CBPF Hickman, I.A.B.e CBPF Kneipp, M.A.C. CBPF Kobe, D. IFT UNESP Kunk, V. IFUSP Kurobart, SM. IFUSP Kõrbde,R. IFQSC Lima, A.F.de IFUSP lira, MB. UC Luanda, J. IEAV-CTA Macedo, A.A.S. PUCRJ Maciel, A. CBPF Magalhães, N.S. IFUSP Mardooes, A.A. UC Moricone, L. PUCRJ MarvuIIc,V. IFUSP Melter J.C. UFR-RJ Mendes, R.dos S. IFUSP Menon, M.J. UNICAMP Menon, M.L.T. UNICAMP Montalvo, J.E.C. IFUSP Moraes Filho, A.Z. IFT UNESP Moreno, E. La Plata IX Nascimento, J.R.S.do ÜFPB Negrini Neto, O. IFUSP Piquini, P.C- IFUSP Pierri.M. CBPF Ramos, R-de O. IFÜSP Ricci, T.S.F. ÜFRGS Ricotta, R.M. IFT ÜNESP Rivefles, Vde 0. IFUSP Rodrigues, R.L. IFT ÜNESP Sabrò,A. PUCRJ Sandoval Junior, L. IFUSP Schaposnik, F. Ia Plata Sigaud Filho, C UFRJ Silva, A.Jda IFUSP Souza, C.F.de UFRJ Souzc, M.M.de UFES Suzuki, A.T. **' " ÜNESP Takamura, F.I. PUCRJ Teotònio Sobrinho, P. I^USP Thomaz, M.T.C.S. UFF Valle, J.L.M. CBPF Vanhecke, F.J. UFRJ Zimmerman, A.H. IFT UNESP CAB: Centro Atômico .e Baríloche, 8400 Baríloche- Rio Negro, Argentina. CBPF: Centro Brasileiro de Pesquisas Físi a», rua Dr. Xavier Sigaud, 150, 2290 Rio de Janeiro, RJ, Brasil. IEAV-CTA: Inst. de Estudos Avançados, C. P- 6044, 12231, São José dos Campos, São Paulo, SP, Brasil. IFQSC: Instituto de Física e Química de São Carlos, C. P. 369,13560 São Carlos, SP, Brasil. IFT-UNESP: Instituto de Física Teórica, Universidade Estadual Paulista, ma Pamplona 145, 01405 São Paulo, SP, Brasil. IFUSP: Instituto de Física, Universidade de São Paulo, C. P. 20516, 01498 São Paulo, SP, Brasil. La Plata: Departamento de Física, Universidad Nacional de La Plata, C. C. 67,1900, La Plata, Argentina. PUCRJ: Departamento de Física, Pontifícia Universiade Católica, C P. 38071, 22453, Rio de Janeiro, RJ, Brasil. UC: Departamento de Física, Universidade do Chile, Ca :11a 54S7, Santiago, Chile UFES: Departamento de Física, Universidade Federal do Espirito Santo, Av. Fernando Ferrari s/n, 29000 Vitória, ES, Brasil. UFF: Instituto de Física, Universidade Federal Fluminense, Outeiro de São João B tista s/n, 24020 Niterói, RJ, Brasil. UFPA: Departamento de Física, Universidade Federal do Pará, C. P. 6S, 6600 Belém, PA, Brasil. UFPB: Departamento de Física, Universidade Federal ca Paraíba, 5S0OO João Pessoa, PB, Brasil. UFRJ: Instituto de Física, Universidade Federal do Rio de Janeiro, C. P. 6852$, 21944 Rio de Janeiro, RJ, Brasil. UFRGS: Instituto de Física, Universidade Federal do Rio Grande do Sul, C. P. 15051, 91500 Porto Alegre, RS, Brasil. UFR-RJ: Departamento de Física, Universidade Federal Rural do Rio de Janeiro, 23460 Itaguaí, RJ, Brasil. UNICAMP: Instituto de Física, Universidade Estadual de Campinas, C. P. 1170, 13100 Campinas, São Paulo, Brasil. XI CONTENTS Preface v Lecturers and Topics vi Participants vii Classical and Quantum Dynamics of Constrained Systems 1 H. 0. Girotti Analysis on Infinite-Dimension Manifolds — Schrõdinger Representation for Quantized Fields 78 R.Jackiw Quantum Field Theory in Flat Robertson-Walker Space-Time: Functional Schrõdinger Picture 144 So-Young Pi Rational Conformai Theories Involving a U(l) Current Algebra 196 Ivan T. Todorov Yang-Baxter Algebra — Integrable Systems — Conformai Quantum Field Theories 246 M. Karowski Dynamical Parasupersymmetries in Quantum Mechanics 291 Stephane Durand and Luc Vinet Introduction to String Field Theory — 315 Gary T. Horowitz pp Collide: Physics 370 Dan Green Strong Interaction Phenomenology 489 Maurice Giffon and Enrico Predazzi QCD and Hadronic Strings 656 Gilles Cohen-Tannoudji XB Topological Field Theories and Two-Dimensional Instantons 683 Fidel A. Schaposnik Gravity in 2 + 1 Dimensions 70S Ph. de Sousa Gerbert Parafermionic Conformai Field Theory 719 V. Kurak Author Index 731 CLASSICAL AND QUANTUM DYKAMICS OF CONSTRAINED SYSTEMS H.O.Cirotti Institute de Física Universidade Federal do Rio Grande do Sul Caixa Postal 15051, 9150C Porto Alegre, RS BRASIL Lectures delivered at the Vth Sinner School Jorge Andre Svieca, Section: Particles and Fields. Campos do Jordão, SP, Brazil (1989). CONTENTS I. CLASSICAL DYNAMICS OF CONSTRAINED SYSTEMS 1.1. Singular Systems. Definition. 1.2. Symmetry Transformations 1.3. Hamiltonian Formulation of Constrained Systems 1.4. Reparametrization Transformations 1.5. Gauge Fixing II. QUANTIZATION OF CONSTRAINED SYSTEMS II. 1. The Dine Bracket Quantization Procedure 11.2. Illustrative Example: Canonical Quantization of a Self-Dual Field Theory 11.3. Functional Quantization 11.4. Quantization of First-Class Systems in Non-Canonical Gauges. BRST Quantization. III. ALTERNATIVE FORMULATIONS OF ANOMALOUS CHIRAL GAUGE THEORIES 111.1. Preliminaries 111.2. The Chiral Schwinger Model 111.3. Canonical Quantization of the Gaugi Invariant Chiral Schwinger Model 111.4. The Fermion Operators of the GNI Chiral Schwinger Model I. CLASSICAL DYNAMICS OF CONSTRAINED SYSTEMS I.I. Singular Systems. Definition In order to treat simultaneously physical systems possessing either a finite or an infinite number of degrees of freedom, we found convenient to introduce the following notation: Q (T), A = 1,...,N, denote the coordinates (or fields) spanning the configuration space of the physical system.