The Noether Theorems Invariance and Conservation Laws in the Twentie
In 1915 Emmy Noether was invited by Klein and Hilbert to Göttingen to assist them in understanding the law of conservation of energy in Einstein’s new general theory of relativity. She succeeded brilliantly. In the Invariante Variationsprobleme, published
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Emmy Noether (1882–1935) (photograph courtesy of the Emmy Noether Foundation, Bar Ilan University)
Yvette Kosmann-Schwarzbach
The Noether Theorems Invariance and Conservation Laws in the Twentieth Century
Translated by Bertram E. Schwarzbach
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Yvette Kosmann-Schwarzbach Centre de Mathématiques Laurent Schwartz École Polytechnique 91128 Palaiseau France [email protected]
Bertram E. Schwarzbach (Translator)
e-ISBN 978-0-387-87868-3 ISBN 978-0-387-87867-6 DOI 10.1007/978-0-387-87868-3 Springer New York Dordrecht Heidelberg London Mathematics Subject Classification (2010): 01-02, 22-03, 22E70, 49-03, 49S05, 70-03, 70H03, 70H33, 83-03
© Springer Science+Business Media, LLC 2011 All rights reserved. This work may not be translated or copied in whole or in part without the written permission of the publisher (Springer Science+Business Media, LLC, 233 Spring Street, New York, NY 10013, USA), except for brief excerpts in connection with reviews or scholarly analysis. Use in connection with any form of information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed is forbidden. The use in this publication of trade names, trademarks, service marks, and similar terms, even if they are not identied as such, is not to be taken as an expression of opinion as to whether or not they are subject to proprietary rights. Printed on acid-free paper Springer is part of Springer Science+Business Media (www.springer.com)
In memory of Yseult d′′ r who liked science as well as history
Preface
What follows thus depends upon a combination of the methods of the formal calculus of variations and of Lie's theory of groups. Emmy Noether, 1918
This book is about a fundamental text containing two theorems and their converses which established the relation between symmetries and conservation laws for variational problems. These theorems, whose importance remained obscure for decades, eventually acquired a considerable influence on the development of modern theoretical physics, and their history is related to numerous questions in physics, in mechanics and in mathematics. This text is the article “Invariante Variationsprobleme” by Emmy Noether, which was published in 1918 in the G¨ottinger Nachrichten, and of which we present an English translation in Part I of this book. The translation of Noether’s article is followed, in Part II, by a detailed analysis of its inception, as well as an account of its reception in the scientific community. As the background to Noether’s research, we sketch some developments in the theory of invariants in the nineteeth century which culminated in the definition and study of differential invariants, we discuss several works in mechanics dating from the beginning of the twentieth century in which
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