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Combining the corrected editions of both volumes on classical physics of Thirring's course in mathematical physics, this treatment of classical dynamical systems employs analysis on manifolds to provide the mathematical setting for discussions of Hamiltonian systems. Problems discussed in detail include nonrelativistic motion of particles and systems, relativistic motion in electromagnetic and gravitational fields, and the structure of black holes. The treatment of classical fields uses differential geometry to examine both Maxwell's and Einstein's equations with new material added on guage theory.
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Walter Thirring A Course in Mathematical Physics 2 Classical Field Theory Translated by Evans M. Harrell Springer-Verlag New York• Wien Dr. Walter Thirring Dr. Evans Harrell Institute for Theoretical Physics University of Vienna Austria The Johns Hopkins University Baltimore, Maryland USA Translation of Lehrbuch der Mathematischen Physik Rand 2: Klassische Feldtheorie Wien-New York: Springer-Verlag 1978 by Springer-Verlag! Wien ISBN 3-211-81475-2 Springer-Verlag Wien New York ISBN 0-387-81475-2 Springer-Verlag New York Wien © 1978 Library of Congress Cataloging in Publication Data (Revised) 1927Thirring, Walter £ A course in mathematical physics. Translation of Lehrbuch der mathematischen Physik. Bibliography: p. Includes index. CONTENTS: 1. Classical dynamical systems. —2. Classical field theory. I. Title. QC2O.T4513 530.1'5 78-16172 With 70 Figures All rights reserved. No part in any © of this book may be translated or reproduced form without written permission from Springer-Verlag. 1979 by Springer-Verlag New York Inc. Printed in United States of America. 987654321 ISBN 0-387-81532-5 Springer-Verlag New York ISBN 3-211-81532-5 Springer-Verlag Wien Preface This volume presents the classical theory of fields with the methods of modern differential geometry. This approach not only has conceptual advantages, but is also technically convenient for the solution of Maxwell's and Einstein's equations: Cartan's formalism sweeps away the jumble of indices and allows the geometrical meaning of the observables to emerge. The need to accommodate all the material in a one-semester course and the desirability of a concise presentation have necessitated a drastic selection of topics; many an expert with a pet topic will no doubt be reluctant to forgive my sins of omission. Continuing in the spirit of the first volume, I have attempted to introduce only what can strictly be deduced from first principles. Those parts of the theory described by W. Pauli as "wishful mathematics" are left out. In order that this selection does not leave the material sterile, intuitive arguments are also presented, with the-help of which manyof the mathematical intricacies in the more complicated problems can be glossed over. Classical field theory almost attains the ideal of a complete, deductive theory, but not quite. Occasionally the singularity of a hr potential causes difficulties for electrodynamics as well as for gravitation. This seems to be a characteristic of all physical theories; although they may encompass large portions of our knowledge, a small kernel of incompleteness is inevitably left. The mathematical methods will be briefly recapitulated, though for details and a systematic presentation of the terminology, please -refer to volume 1 (denoted below by I). The references to the literature, denoted by square brackets [], are to be found at the end, as is a list of more recent works on the iv Preface subject. An exhaustive b