The Noether Theorems

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The Noether Theorems

Author : Yvette Kosmann-Schwarzbach
Publisher : Springer Science & Business Media
ISBN 13 : 0387878688
Total Pages : 205 pages
Book Rating : 4.3/5 (878 download)

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Book Synopsis The Noether Theorems by : Yvette Kosmann-Schwarzbach

Download or read book The Noether Theorems written by Yvette Kosmann-Schwarzbach and published by Springer Science & Business Media. This book was released on 2010-11-17 with total page 205 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Emmy Noether's Wonderful Theorem

Author : Dwight E. Neuenschwander
Publisher : JHU Press
ISBN 13 : 1421422689
Total Pages : 338 pages
Book Rating : 4.4/5 (214 download)

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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.

The Philosophy and Physics of Noether's Theorems

Author : James Read
Publisher : Cambridge University Press
ISBN 13 : 1108786812
Total Pages : 388 pages
Book Rating : 4.1/5 (87 download)

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Book Synopsis The Philosophy and Physics of Noether's Theorems by : James Read

Download or read book The Philosophy and Physics of Noether's Theorems written by James Read and published by Cambridge University Press. This book was released on 2022-08-31 with total page 388 pages. Available in PDF, EPUB and Kindle. Book excerpt: In 1918, Emmy Noether, in her paper Invariante Variationsprobleme, proved two theorems (and their converses) on variational problems that went on to revolutionise theoretical physics. 100 years later, the mathematics of Noether's theorems continues to be generalised, and the physical applications of her results continue to diversify. This centenary volume brings together world-leading historians, philosophers, physicists, and mathematicians in order to clarify the historical context of this work, its foundational and philosophical consequences, and its myriad physical applications. Suitable for advanced undergraduate and graduate students and professional researchers, this is a go-to resource for those wishing to understand Noether's work on variational problems and the profound applications which it finds in contemporary physics.

Noether's Theorems

Author : Gennadi Sardanashvily
Publisher : Springer
ISBN 13 : 9462391718
Total Pages : 297 pages
Book Rating : 4.4/5 (623 download)

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Book Synopsis Noether's Theorems by : Gennadi Sardanashvily

Download or read book Noether's Theorems written by Gennadi Sardanashvily and published by Springer. This book was released on 2016-03-18 with total page 297 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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-relativistic mechanics, gauge theory, gravitation theory and topological field theory with emphasis on energy and energy-momentum conservation laws. Within this general context the first and second Noether theorems are treated in the very general setting of reducible degenerate graded Lagrangian theory.

Noether's Theorem and Symmetry

Author : P.G.L. Leach
Publisher : MDPI
ISBN 13 : 3039282344
Total Pages : 186 pages
Book Rating : 4.0/5 (392 download)

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Book Synopsis Noether's Theorem and Symmetry by : P.G.L. Leach

Download or read book Noether's Theorem and Symmetry written by P.G.L. Leach and published by MDPI. This book was released on 2020-03-05 with total page 186 pages. Available in PDF, EPUB and Kindle. Book excerpt: In Noether's original presentation of her celebrated theorem of 1918, allowances were made for the dependence of the coefficient functions of the differential operator which generated the infinitesimal transformation of the Action Integral upon the derivatives of the dependent variable(s), the so-called generalized, or dynamical, symmetries. A similar allowance is to be found in the variables of the boundary function, often termed a gauge function by those who have not read the original paper. This generality was lost after texts such as those of Courant and Hilbert or Lovelock and Rund confined attention to only point transformations. In recent decades, this diminution of the power of Noether's Theorem has been partly countered, in particular, in the review of Sarlet and Cantrijn. In this Special Issue, we emphasize the generality of Noether's Theorem in its original form and explore the applicability of even more general coefficient functions by allowing for nonlocal terms. We also look at the application of these more general symmetries to problems in which parameters or parametric functions have a more general dependence upon the independent variables.

The Philosophy and Physics of Noether's Theorems

Author : James Read
Publisher : Cambridge University Press
ISBN 13 : 1108486231
Total Pages : 387 pages
Book Rating : 4.1/5 (84 download)

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Book Synopsis The Philosophy and Physics of Noether's Theorems by : James Read

Download or read book The Philosophy and Physics of Noether's Theorems written by James Read and published by Cambridge University Press. This book was released on 2022-09-29 with total page 387 pages. Available in PDF, EPUB and Kindle. Book excerpt: A centenary volume that celebrates, extends and applies Noether's 1918 theorems with contributions from world-leading researchers.

Gauge Invariance Approach to Acoustic Fields

Author : Woon Siong Gan
Publisher : Springer
ISBN 13 : 9811387516
Total Pages : 169 pages
Book Rating : 4.8/5 (113 download)

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Book Synopsis Gauge Invariance Approach to Acoustic Fields by : Woon Siong Gan

Download or read book Gauge Invariance Approach to Acoustic Fields written by Woon Siong Gan and published by Springer. This book was released on 2019-07-31 with total page 169 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book highlights the symmetry properties of acoustic fields and describes the gauge invariance approach, which can be used to reveal those properties. Symmetry is the key theoretical framework of metamaterials, as has been demonstrated by the successful fabrication of acoustical metamaterials. The book first provides the necessary theoretical background, which includes the covariant derivative, the vector potential, and invariance in coordinate transformation. This is followed by descriptions of global gauge invariance (isotropy), and of local gauge invariance (anisotropy). Sections on time reversal symmetry, reflection invariance, and invariance of finite amplitude waves round out the coverage.

Emmy Noether

Author : Emmy Noether
Publisher : Marcel Dekker
ISBN 13 :
Total Pages : 216 pages
Book Rating : 4.3/5 (91 download)

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Book Synopsis Emmy Noether by : Emmy Noether

Download or read book Emmy Noether written by Emmy Noether and published by Marcel Dekker. This book was released on 1981 with total page 216 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Emmy Noether 1882–1935

Author : DICK
Publisher : Springer Science & Business Media
ISBN 13 : 1468405357
Total Pages : 213 pages
Book Rating : 4.4/5 (684 download)

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Book Synopsis Emmy Noether 1882–1935 by : DICK

Download or read book Emmy Noether 1882–1935 written by DICK and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 213 pages. Available in PDF, EPUB and Kindle. Book excerpt: N 1964 at the World's Fair in New York I City one room was dedicated solely to mathematics. The display included a very at tractive and informative mural, about 13 feet long, sponsored by one of the largest com puter manufacturing companies and present ing a brief survey of the history of mathemat ics. Entitled, "Men of Modern Mathematics," it gives an outline of the development of that science from approximately 1000 B. C. to the year of the exhibition. The first centuries of this time span are illustrated by pictures from the history of art and, in particular, architec ture; the period since 1500 is illuminated by portraits of mathematicians, including brief descriptions of their lives and professional achievements. Close to eighty portraits are crowded into a space of about fourteen square feet; among them, only one is of a woman. Her face-mature, intelligent, neither pretty nor handsome-may suggest her love of sci- 1 Emmy Noether ence and creative gift, but certainly reveals a likeable personality and a genuine kindness of heart. It is the portrait of Emmy Noether ( 1882 - 1935), surrounded by the likenesses of such famous men as Joseph Liouville (1809-1882), Georg Cantor (1845-1918), and David Hilbert (1862 -1943). It is accom panied by the following text: Emmy Noether, daughter of the mathemati cian Max, was often called "Der Noether," as if she were a man.

Groups and Symmetries

Author : Yvette Kosmann-Schwarzbach
Publisher : Springer Science & Business Media
ISBN 13 : 0387788662
Total Pages : 207 pages
Book Rating : 4.3/5 (877 download)

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Book Synopsis Groups and Symmetries by : Yvette Kosmann-Schwarzbach

Download or read book Groups and Symmetries written by Yvette Kosmann-Schwarzbach and published by Springer Science & Business Media. This book was released on 2009-10-16 with total page 207 pages. Available in PDF, EPUB and Kindle. Book excerpt: - Combines material from many areas of mathematics, including algebra, geometry, and analysis, so students see connections between these areas - Applies material to physics so students appreciate the applications of abstract mathematics - Assumes only linear algebra and calculus, making an advanced subject accessible to undergraduates - Includes 142 exercises, many with hints or complete solutions, so text may be used in the classroom or for self study

The Noether Theorems

Author : Yvette Kosmann-Schwarzbach
Publisher :
ISBN 13 :
Total Pages : 213 pages
Book Rating : 4.:/5 (99 download)

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Book Synopsis The Noether Theorems by : Yvette Kosmann-Schwarzbach

Download or read book The Noether Theorems written by Yvette Kosmann-Schwarzbach and published by . This book was released on 2010 with total page 213 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 vario.

Energy Momentum Tensors

Author : Robert Hermann
Publisher : Math-Sci Press
ISBN 13 : 9780915692033
Total Pages : 132 pages
Book Rating : 4.6/5 (92 download)

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Book Synopsis Energy Momentum Tensors by : Robert Hermann

Download or read book Energy Momentum Tensors written by Robert Hermann and published by Math-Sci Press. This book was released on 1973 with total page 132 pages. Available in PDF, EPUB and Kindle. Book excerpt:

The Brauer-Hasse-Noether Theorem in Historical Perspective

Author : Peter Roquette
Publisher : Springer Science & Business Media
ISBN 13 : 3540269681
Total Pages : 92 pages
Book Rating : 4.5/5 (42 download)

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Book Synopsis The Brauer-Hasse-Noether Theorem in Historical Perspective by : Peter Roquette

Download or read book The Brauer-Hasse-Noether Theorem in Historical Perspective written by Peter Roquette and published by Springer Science & Business Media. This book was released on 2006-03-30 with total page 92 pages. Available in PDF, EPUB and Kindle. Book excerpt: The unpublished writings of Helmut Hasse, consisting of letters, manuscripts and other papers, are kept at the Handschriftenabteilung of the University Library at Göttingen. Hasse had an extensive correspondence; he liked to exchange mathematical ideas, results and methods freely with his colleagues. There are more than 8000 documents preserved. Although not all of them are of equal mathematical interest, searching through this treasure can help us to assess the development of Number Theory through the 1920s and 1930s. The present volume is largely based on the letters and other documents its author has found concerning the Brauer-Hasse-Noether Theorem in the theory of algebras; this covers the years around 1931. In addition to the documents from the literary estates of Hasse and Brauer in Göttingen, the author also makes use of some letters from Emmy Noether to Richard Brauer that are preserved at the Bryn Mawr College Library (Pennsylvania, USA).

The Universe of General Relativity

Author : A.J. Kox
Publisher : Springer Science & Business Media
ISBN 13 : 0817644547
Total Pages : 384 pages
Book Rating : 4.8/5 (176 download)

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Book Synopsis The Universe of General Relativity by : A.J. Kox

Download or read book The Universe of General Relativity written by A.J. Kox and published by Springer Science & Business Media. This book was released on 2006-09-10 with total page 384 pages. Available in PDF, EPUB and Kindle. Book excerpt: Outgrowth of 6th Int'l Conference on the History of General Relativity, held in Amsterdam on June 26-29, 2002 Contributions from notable experts offer both new and historical insights on gravitation, general relativity, cosmology, unified field theory, and the history of science Topics run gamet from detailed mathematical discussions to more personal recollections of relativity as seen through the eyes of the public and renowned relativists

Classical Dynamics

Author : Jorge V. José
Publisher : Cambridge University Press
ISBN 13 : 9780521636360
Total Pages : 702 pages
Book Rating : 4.6/5 (363 download)

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Book Synopsis Classical Dynamics by : Jorge V. José

Download or read book Classical Dynamics written by Jorge V. José and published by Cambridge University Press. This book was released on 1998-08-13 with total page 702 pages. Available in PDF, EPUB and Kindle. Book excerpt: A comprehensive graduate-level textbook on classical dynamics with many worked examples and over 200 homework exercises, first published in 1998.

Emmy Noether

Author : M. B. W. Tent
Publisher : CRC Press
ISBN 13 : 1439865345
Total Pages : 184 pages
Book Rating : 4.4/5 (398 download)

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Book Synopsis Emmy Noether by : M. B. W. Tent

Download or read book Emmy Noether written by M. B. W. Tent and published by CRC Press. This book was released on 2008-10-10 with total page 184 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book, written primarily for the young adult reader, tells the life story of Emmy Noether, the most important female mathematician of our time. Because no one expected her to grow into an important scientist, the records of her early life are sketchy. After all, it was assumed that she would grow up to be a wife and mother. Instead, she was a g

Physics from Symmetry

Author : Jakob Schwichtenberg
Publisher : Springer
ISBN 13 : 3319666312
Total Pages : 287 pages
Book Rating : 4.3/5 (196 download)

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Book Synopsis Physics from Symmetry by : Jakob Schwichtenberg

Download or read book Physics from Symmetry written by Jakob Schwichtenberg and published by Springer. This book was released on 2017-12-01 with total page 287 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is a textbook that derives the fundamental theories of physics from symmetry. It starts by introducing, in a completely self-contained way, all mathematical tools needed to use symmetry ideas in physics. Thereafter, these tools are put into action and by using symmetry constraints, the fundamental equations of Quantum Mechanics, Quantum Field Theory, Electromagnetism, and Classical Mechanics are derived. As a result, the reader is able to understand the basic assumptions behind, and the connections between the modern theories of physics. The book concludes with first applications of the previously derived equations. Thanks to the input of readers from around the world, this second edition has been purged of typographical errors and also contains several revised sections with improved explanations.