Emmy Noether's Wonderful Theorem

4.20 ( 76 Ratings by Goodreads)
Emmy Noether's Wonderful Theorem
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Emmy Noether's Wonderful Theorem

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4.20 (76 Ratings by Goodreads)
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Published: 28 April, 2017
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Description

"In the judgment of the most competent living mathematicians, Fraulein 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 Gottingen 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.
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Type Book
ISBN13 9781421422671
ISBN10 1421422670
Number Of Pages 344
Item Weight 454 g
Product Dimensions 152 x 229 x 21 mm
Publisher / Reseller Johns Hopkins University Press
Format paperback
Edition revised and updated edition
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Media Reviews

As this book is well written and contains a very good set of exercises, it can serve as the primary text for a special topics course.
—Choice
Nadis gives no technical details, but Neuenschwander does, in a book for physics majors with a strong background in mathematics; the book does not shy away from Lie groups and the study of invariants. This new edition delves into distinctions between two Noether theorems and adds more exercises, references, and details.
—Mathematics Magazine
Neuenschwander sets out from the beginning to help the reader who must be familiar with calculus and a few other standard topics, but who is not yet fluent in these areas. His role is to be the teacher on the side, prompting the reader with interesting observations and questions. He anticipates problems, guides you, yet also makes you think things through. Not only a very worthwhile read for its content but also for its style.
—Ken Zetie, St. Paul's School, Mathematical Gazette
Well-written... Throughout there is reference to the life of Emmy Noether, including the many difficulties related to being a woman in a man's world... I am glad her story is given an airing here as she fails to be as famous as she undoubtedly should be.
—Phil Dyke, FIMA, Mathematics Today
Technical and yet ultimately poetic book on Emmy Neother's wonderful theorems... Neuenschwander's work is recommended for anyone who wants to gain a deeper understanding and appreciation of the physics and mathematics behind Emmy Noether's work, as well as the particular challenges she faced in her life.
—Miriam R. Aczel, Centre for Environmental Policy, Imperial College London, Contemporary Physics

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Author's Bio

Dwight E. Neuenschwander is a professor of physics at Southern Nazarene University. He is a columnist for the Observer, the magazine of the Society for Physics Students, and the author of Tensor Calculus for Physics: A Concise Guide.

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