A Course in Mathematical Physics, Vol 2, Classical Field Theory (Walter Thirring) 0387815325.pdf

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 The Johns Hopkins University
University of Vienna Baltimore, Maryland
Austria USA
Translation of Lehrbuch der Mathematischen Physik
Rand 2: Klassische Feldtheorie
Wien-New York: Springer-Verlag 1978
©1978by Springer-Verlag! Wien
ISBN 3-211-81475-2 Springer-Verlag Wien New York
ISBN 0-387-81475-2 Springer-Verlag New York Wien
Library of Congress Cataloging in Publication Data (Revised)
Thirring, Walter £ 1927-
A course in mathematical physics.
Translation of Lehrbuch der mathematischen Physik.
Bibliography: p.
Includes index.
CONTENTS:1. Classical dynamical systems. —2.
Classical field theory.
.
'5 78-16172
With 70 Figures
All rights reserved.
Nopart of this book may betranslated or reproduced
inany form without written permission from Springer-Verlag.
©1979by Springer-Verlag New York Inc.
Printed in United States of America.
987654321
ISBN0-387-81532-5 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 modate 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 theor