Emmy Noether's Wonderful Theorem

Emmy Noether's Wonderful Theorem
Author :
Publisher : JHU Press
Total Pages : 338
Release :
ISBN-10 : 9781421422688
ISBN-13 : 1421422689
Rating : 4/5 (88 Downloads)

Book Synopsis Emmy Noether's Wonderful Theorem by : Dwight E. Neuenschwander

Download or read book Emmy Noether's Wonderful Theorem written by Dwight E. Neuenschwander and published by JHU Press. This book was released on 2017-04-01 with total page 338 pages. Available in PDF, EPUB and Kindle. Book excerpt: One of the most important—and beautiful—mathematical solutions ever devised, Noether’s theorem touches on every aspect of physics. "In the judgment of the most competent living mathematicians, Fräulein Noether was the most significant creative mathematical genius thus far produced since the higher education of women began."—Albert Einstein The year was 1915, and the young mathematician Emmy Noether had just settled into Göttingen University when Albert Einstein visited to lecture on his nearly finished general theory of relativity. Two leading mathematicians of the day, David Hilbert and Felix Klein, dug into the new theory with gusto, but had difficulty reconciling it with what was known about the conservation of energy. Knowing of her expertise in invariance theory, they requested Noether’s help. To solve the problem, she developed a novel theorem, applicable across all of physics, which relates conservation laws to continuous symmetries—one of the most important pieces of mathematical reasoning ever developed. Noether’s “first” and “second” theorem was published in 1918. The first theorem relates symmetries under global spacetime transformations to the conservation of energy and momentum, and symmetry under global gauge transformations to charge conservation. In continuum mechanics and field theories, these conservation laws are expressed as equations of continuity. The second theorem, an extension of the first, allows transformations with local gauge invariance, and the equations of continuity acquire the covariant derivative characteristic of coupled matter-field systems. General relativity, it turns out, exhibits local gauge invariance. Noether’s theorem also laid the foundation for later generations to apply local gauge invariance to theories of elementary particle interactions. In Dwight E. Neuenschwander’s new edition of Emmy Noether’s Wonderful Theorem, readers will encounter an updated explanation of Noether’s “first” theorem. The discussion of local gauge invariance has been expanded into a detailed presentation of the motivation, proof, and applications of the “second” theorem, including Noether’s resolution of concerns about general relativity. Other refinements in the new edition include an enlarged biography of Emmy Noether’s life and work, parallels drawn between the present approach and Noether’s original 1918 paper, and a summary of the logic behind Noether’s theorem.


Emmy Noether's Wonderful Theorem Related Books

Emmy Noether's Wonderful Theorem
Language: en
Pages: 338
Authors: Dwight E. Neuenschwander
Categories: Science
Type: BOOK - Published: 2017-04-01 - Publisher: JHU Press

DOWNLOAD EBOOK

One of the most important—and beautiful—mathematical solutions ever devised, Noether’s theorem touches on every aspect of physics. "In the judgment of the
Noether's Theorems
Language: en
Pages: 304
Authors: Gennadi Sardanashvily
Categories: Mathematics
Type: BOOK - Published: 2016-03-18 - Publisher: Springer

DOWNLOAD EBOOK

The book provides a detailed exposition of the calculus of variations on fibre bundles and graded manifolds. It presents applications in such area's as non-rela
The Noether Theorems
Language: en
Pages: 211
Authors: Yvette Kosmann-Schwarzbach
Categories: Mathematics
Type: BOOK - Published: 2010-11-17 - Publisher: Springer Science & Business Media

DOWNLOAD EBOOK

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 t
The Philosophy and Physics of Noether's Theorems
Language: en
Pages: 388
Authors: James Read
Categories: Science
Type: BOOK - Published: 2022-08-31 - Publisher: Cambridge University Press

DOWNLOAD EBOOK

In 1918, Emmy Noether, in her paper Invariante Variationsprobleme, proved two theorems (and their converses) on variational problems that went on to revolutioni
Noether's Theorem and Symmetry
Language: en
Pages: 186
Authors: P.G.L. Leach
Categories: Science
Type: BOOK - Published: 2020-03-05 - Publisher: MDPI

DOWNLOAD EBOOK

In Noether's original presentation of her celebrated theorem of 1918, allowances were made for the dependence of the coefficient functions of the differential o