The Noether Theorems : Invariance and Conservation Laws in the 20th Century (Sources and Studies in the History of Mathematics and Physical Sciences)

Kosmann-Schwarzbach, Yvette

Springer（2010/11発売）

• 製本 Paperback:紙装版/ペーパーバック版／ページ数 206 p.
• 商品コード 9780387878676

基本説明

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.

Full Description

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.