The Noether Theorems - Yvette Kosmann-Schwarzbach

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Résumé :
In 1915 and 1916 Emmy Noether was asked by Felix Klein and David Hilbert to assist them in understanding issues involved in any attempt to formulate a general theory of relativity, in particular the new ideas of Einstein. She was consulted particularly over the difficult issue of the form a law of conservation of energy could take in the new theory, and she succeeded brilliantly, finding two deep theorems. But between? 1916 and 1950, the theorem was poorly understood and Noether's name disappeared almost entirely. People like Klein and Einstein did little more then mention her name in the various popular or historical accounts they wrote. Worse, earlier attempts which had been eclipsed by Noether's achievements were remembered, and sometimes figure in quick historical accounts of the time. This book carries a translation of Noether's original paper into English, and then describes the strange history of its reception and the responses to her work. Ultimately the theorems became decisive in a shift from basing fundamental physics on conservations laws to basing it on symmetries, or at the very least, in thoroughly explaining the connection between these two families of ideas. The real significance of this book is that it shows very clearly how long it took before mathematicians and physicists began to recognize the seminal importance of Noether's results. This book is thoroughly researched and provides careful documentation of the textbook literature. Kosmann-Schwarzbach has thus thrown considerable light on this slow dance in which the mathematical tools necessary to study symmetry properties and conservation laws were apparently provided long before the orchestra arrives and the party begins.

Biographie:
A former student of the ?cole Normale Sup?rieure in Paris, Yvette Kosmann-Schwarzbach holds a Doctorat d'?tat in mathematics as well as a degree in physics from the University of Paris. She has been a professor of mathematics at the University of Lille, at Brooklyn College of the City University of New York, and at the ?cole Polytechnique (France). She has organized numerous conferences, and has held visiting positions and lectured on four continents.The author of the historical study, The Noether Theorems, Invariance and Conservation Laws in the Twentieth Century (Sources and Studies in the History of Mathematics and Physical Sciences), she has published over 90 research articles in differential geometry, algebra and mathematical physics, and has co-edited The Verdier Memorial Conference on Integrable Systems (Progress in Mathematics), Integrability of Nonlinear Systems (Lecture Notes in Physics) and Discrete Integrable Systems (LectureNotes in Physics)....

Sommaire:
Preface.-Acknowledgements.- I. Invariant Variational Problems. II.- Invariance and Conservation Laws in the Twentieth Century. The Inception and Reception of the Noether Theorems. - 1. The Inception of the Noether Theorems. -2. The Noether Theorems.-3. The Noether Theorems as Seen by Contemporaries and by Historians of Science.-4. From Bessel-Hagen to Hill, 1921-1951.-5. The Reception of Noether's First Theorem after 1950.-6. The Reception of Noether's Second Theorem after 1950.-7. After 1970-Genuine Generalizations.-Conclusion.-Appendix I. Postcard from Noether to Klein.-Appendix II. Letter from Noether to Klein. -Appendix III. Letter from Klein to Pauli.-Appendix IV. Letter from Noether to Einstein.-Lectures at the Mathematical Society of G?ttingen.-References.-Index.