Table Of Content

7689tp.indd 1 5/3/10 8:54:07 AM World Scientific Lecture Notes in Physics Published titles* Vol. 62: ITEP Lectures on Particle Physics and Field Theory (in 2 Volumes) M A Shifman Vol. 64: Fluctuations and Localization in Mesoscopic Electron Systems M Janssen Vol. 65: Universal Fluctuations: The Phenomenology of Hadronic Matter R Botet and M Ploszajczak Vol. 66: Microcanonical Thermodynamics: Phase Transitions in “Small” Systems D H E Gross Vol. 67: Quantum Scaling in Many-Body Systems M A Continentino Vol. 69: Deparametrization and Path Integral Quantization of Cosmological Models C Simeone Vol. 70: Noise Sustained Patterns: Fluctuations and Nonlinearities Markus Loecher Vol. 71: The QCD Vacuum, Hadrons and Superdense Matter (2nd ed.) Edward V Shuryak Vol. 72: Massive Neutrinos in Physics and Astrophysics (3rd ed.) R Mohapatra and P B Pal Vol. 73: The Elementary Process of Bremsstrahlung W Nakel and E Haug Vol. 74: Lattice Gauge Theories: An Introduction (3rd ed.) H J Rothe Vol. 75: Field Theory: A Path Integral Approach (2nd ed.) A Das Vol. 76: Effective Field Approach to Phase Transitions and Some Applications to Ferroelectrics (2nd ed.) J A Gonzalo Vol. 77: Principles of Phase Structures in Particle Physics H Meyer-Ortmanns and T Reisz Vol. 78: Foundations of Quantum Chromodynamics: An Introduction to Perturbation Methods in Gauge Theories (3rd ed.) T Muta Vol. 79: Geometry and Phase Transitions in Colloids and Polymers W Kung Vol. 80: Introduction to Supersymmetry (2nd ed.) H J W Müller-Kirsten and A Wiedemann Vol. 81: Classical and Quantum Dynamics of Constrained Hamiltonian Systems H J Rothe and K D Rothe *For the complete list of published titles, please visit http://www.worldscibooks.com/series/lnp_series.shtml EH - Classical and Quantum Dynamics.pmd 2 2/8/2010, 3:10 PM World Scientific Lecture Notes in Physics – Vol. 81 World Scientific NEW JERSEY • LONDON • SINGAPORE • BEIJING • SHANGHAI • HONG KONG • TAIPEI • CHENNAI 7689tp.indd 2 5/3/10 8:54:07 AM Published by World Scientific Publishing Co. Pte. Ltd. 5 Toh Tuck Link, Singapore 596224 USA office: 27 Warren Street, Suite 401-402, Hackensack, NJ 07601 UK office: 57 Shelton Street, Covent Garden, London WC2H 9HE Library of Congress Cataloging-in-Publication Data Rothe, Heinz J. Classical and quantum dynamics of constrained Hamiltonian systems / by Heinz J Rothe & Klaus D Rothe. p. cm. -- (World scientific lecture notes in physics ; v. 81) Includes bibliographical references and index. ISBN-13: 978-981-4299-64-0 (hardcover : alk. paper) ISBN-10: 981-4299-64-2 (hardcover : alk. paper) 1. Quantum theory. 2. Constrained Hamiltonian systems. 3. Quantum field theory. 4. Gauge field theories. I. Rothe, Klaus D. (Klaus Dieter) II. Title. QC174.125.R68 2010 530.12--dc22 2009052083 British Library Cataloguing-in-Publication Data A catalogue record for this book is available from the British Library. Copyright © 2010 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 photocopying, recording or any information storage and retrieval system now known or to be invented, without written permission from the Publisher. For photocopying of material in this volume, please pay a copying fee through the Copyright Clearance Center, Inc., 222 Rosewood Drive, Danvers, MA 01923, USA. In this case permission to photocopy is not required from the publisher. Printed in Singapore. EH - Classical and Quantum Dynamics.pmd 1 2/8/2010, 3:10 PM To Renate and our children Christine, Stefan and Laura Heinz Rothe To Neusa Maria, and our son Thomas Klaus Rothe TThhiiss ppaaggee iinntteennttiioonnaallllyy lleefftt bbllaannkk Classical and Quantum Dynamics of Constrained Hamiltonian Systems Heinz J. Rothe and Klaus D. Rothe Institut fu¨r Theoretische Physik, Universität Heidelberg, Germany TThhiiss ppaaggee iinntteennttiioonnaallllyy lleefftt bbllaannkk Preface Since the pioneering work of Bergmann in 1949, it has been understood that there exists a direct connection between local symmetries of a Lagrangianand the existence of constraints contained in the Euler-Lagrange equations of mo- tion. It was Dirac who subsequently discussed the Hamiltonian dynamics of constrained systems in a systematic way. Since then numerous papers, with applications to awide rangeof problems,havebeen writtenonthis subject. It is remarkable that even after more than half a century, this subject still raises questions to be answered. ThisbookistheresultoflecturesdeliveredbytheauthorsattheUniversity of Heidelberg. It is intended as an introduction to this interesting field of research,startingfromthe earlyworkofDiracuptomorerecentwork,suchas theField-AntifieldformalismofBatalinandVilkovisky. Alsoincludedisabrief discussion of gauge anomalies within this formalism. Here we have restricted ourselves to the essentials, and have illustrated the ideas in terms of a simple example, the chiral Schwinger model. Greatemphasis is placed ondiscussing the subject of constrainedHamilto- nian systems in a transparent way without becoming too technical. Proofs, as well as examples, are discussed in great detail, at the risc of being sometimes pedantic. Each example has been chosen to illustrate some important point. The book should thus hopefully provide a good basis for master degree and Ph.D students. The book is divided into two parts: part one, involving chapters 1 through 8, deals with the classicaldynamics of constrainedHamiltoniansystems, while the second part is devoted to their quantization. Here it is assumed that the reader is familiar with the Feynman path integral approachto quantization.