The Noether Theorems. Invariance and Conservation Laws in the Twentieth Century

Kosmann-Schwarzbach, Yvette

ISBN 10: 038787867X / ISBN 13: 9780387878676

Verlag: Springer, 2011

Beschreibung

24 x 16 cm. Octavo. 205pp. Bound in glossy yellow boards. Back cover lightly bumped. Part of the book series: Sources and Studies in the History of Mathematics and Physical Sciences. 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 in 1918, she proved a fundamental theorem linking invariance properties and conservation laws in any theory formulated in terms of a variational principle, and she stated a second theorem which put a conjecture of Hilbert in perspective and furnished a proof of a much more general result. This book makes the Invariante Variationsprobleme accessible in an English translation. It presents an analysis of the work of Noether s precursors, reformulates her argument in a more modern mathematical language, and recounts the strange history of the article s reception in the mathematics and physics communities. This study shows how her two theorems ultimately became the basis for any deep understanding of the role of symmetries in both classical and quantum physics. The Noether Theorems, a translation of Les Théorèmes de Noether whose French text has been revised and expanded, provides rich documentation drawn from both primary and secondary sources.

Bestandsnummer des Verkäufers 67386

Bibliografische Details

• Titel: The Noether Theorems. Invariance and Conservation Laws in the Twentieth Century
• Verlag: Springer
• Erscheinungsjahr: 2011
• Sprache: Englisch
• ISBN-10: 038787867X
• ISBN-13: 9780387878676
• Einband: Hardcover
• Zustand: Near Fine
• Verkäuferkataloge:
  • Physics

Über diesen Titel

Inhaltsangabe

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.

Über die Autorin bzw. den Autor

A former student of the École Normale Supérieure in Paris, Yvette Kosmann-Schwarzbach holds a Doctorat d'État 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 École 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).