Emmy Noether's Wonderful Theorem

Author: Dwight E. Neuenschwander

Publisher: JHU Press

ISBN: 1421422670

Category: Mathematics

Page: 344

View: 2179

"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

Author: A. Dick

Publisher: Birkhäuser

ISBN: 9783764305192

Category: Science

Page: 72

View: 9472

Helmut Hasse und Emmy Noether

Author: Helmut Hasse,Emmy Noether,Franz Lemmermeyer,Peter Roquette

Publisher: Universitätsverlag Göttingen

ISBN: 3938616350

Category: Class field theory

Page: 301

View: 3756

Moderne Algebra

Author: Bartel Eckmann L. Van der van der Waerden,Emil Artin,Emmy Noether

Publisher: Springer-Verlag

ISBN: 3662364344

Category: Mathematics

Page: 274

View: 3625

Dieser Buchtitel ist Teil des Digitalisierungsprojekts Springer Book Archives mit Publikationen, die seit den Anfängen des Verlags von 1842 erschienen sind. Der Verlag stellt mit diesem Archiv Quellen für die historische wie auch die disziplingeschichtliche Forschung zur Verfügung, die jeweils im historischen Kontext betrachtet werden müssen. Dieser Titel erschien in der Zeit vor 1945 und wird daher in seiner zeittypischen politisch-ideologischen Ausrichtung vom Verlag nicht beworben.

Jüdische Mathematiker in der deutschsprachigen akademischen Kultur

Author: Birgit Bergmann,Moritz Epple

Publisher: Springer-Verlag

ISBN: 3540692525

Category: Mathematics

Page: 236

View: 708

Der Band dokumentiert eine Ausstellung, die im Jahr der Mathematik durch sieben deutsche Städte tourt. Sie zeigt, welch tragende Rolle jüdische Mathematiker im Kaiserreich und in der Weimarer Republik spielten, und sie erinnert daran, wie sie nach 1933 in die Emigration, zur Flucht und in den Tod getrieben wurden. Dabei wird deutlich, dass jüdische Mathematiker in allen Bereichen tätig waren, und wie unterschiedlich ihre jeweiligen Aktivitäten waren. Das widerlegt jedes Klischee über ihren angeblich besonderen Charakter in der Mathematik.

Shattered Symmetry

Group Theory From the Eightfold Way to the Periodic Table

Author: Pieter Thyssen,Arnout Ceulemans

Publisher: Oxford University Press

ISBN: 019062017X

Category: Science

Page: 400

View: 2175

The standard model of subatomic particles and the periodic table of the atoms have the common goal to bring order in the bewildering chaos of the constituents of matter. Their success relies on the presence of fundamental symmetries in their core. The purpose of the book is to share the admiration for the power and the beauty of these symmetries. The reader is taken on a journey from the basic geometric symmetry group of a circle to the sublime dynamic symmetries that govern the motions of the particles. The trail follows the lines of parentage linking groups upstream to the unitary symmetry of the eightfold way of quarks, and to the four-dimensional symmetry of the hydrogen atom. Along the way the theory of symmetry groups is gradually introduced with special emphasis on graphical representations. The final challenge is to open up the structure of Mendeleev's table which goes beyond the symmetry of the hydrogen atom. Breaking this symmetry to accommodate the multi-electron atoms requires to leave the common ground of linear algebras and explore the potential of non-linearity.

Lectures of Sidney Coleman on Quantum Field Theory

Foreword by David Kaiser

Author: Bryan Gin-ge Chen,David Derbes,David Griffiths,Brian Hill,Richard Sohn,Yuan-Sen Ting

Publisher: World Scientific Publishing

ISBN: 9814635529

Category: Science

Page: 1196

View: 624

'Sidney Coleman was the master teacher of quantum field theory. All of us who knew him became his students and disciples. Sidney’s legendary course remains fresh and bracing, because he chose his topics with a sure feel for the essential, and treated them with elegant economy.' Frank WilczekNobel Laureate in Physics 2004 Sidney Coleman was a physicist's physicist. He is largely unknown outside of the theoretical physics community, and known only by reputation to the younger generation. He was an unusually effective teacher, famed for his wit, his insight and his encyclopedic knowledge of the field to which he made many important contributions. There are many first-rate quantum field theory books (the venerable Bjorken and Drell, the more modern Itzykson and Zuber, the now-standard Peskin and Schroeder, and the recent Zee), but the immediacy of Prof. Coleman's approach and his ability to present an argument simply without sacrificing rigor makes his book easy to read and ideal for the student. Part of the motivation in producing this book is to pass on the work of this outstanding physicist to later generations, a record of his teaching that he was too busy to leave himself.

Stochastic Models, Information Theory, and Lie Groups, Volume 2

Analytic Methods and Modern Applications

Author: Gregory S. Chirikjian

Publisher: Springer Science & Business Media

ISBN: 0817649441

Category: Mathematics

Page: 435

View: 7293

This unique two-volume set presents the subjects of stochastic processes, information theory, and Lie groups in a unified setting, thereby building bridges between fields that are rarely studied by the same people. Unlike the many excellent formal treatments available for each of these subjects individually, the emphasis in both of these volumes is on the use of stochastic, geometric, and group-theoretic concepts in the modeling of physical phenomena. Stochastic Models, Information Theory, and Lie Groups will be of interest to advanced undergraduate and graduate students, researchers, and practitioners working in applied mathematics, the physical sciences, and engineering. Extensive exercises, motivating examples, and real-world applications make the work suitable as a textbook for use in courses that emphasize applied stochastic processes or differential geometry.

Geometrie der Berührungstransformationen

Author: Sophus Lie,Georg Scheffers

Publisher: American Mathematical Soc.

ISBN: 9780821837795

Category: Mathematics

Page: 693

View: 2690

The Geometry of Contact Transformation, Sophus Lie's final work.

Gesammelte Abhandlungen - Collected Papers

Author: Emmy Noether

Publisher: Springer

ISBN: 9783540115045

Category: Mathematics

Page: 777

View: 1257

Emmy Noether (1882-1935) was one of the most influential mathematicians of the 20th century. The development of abstract algebra, which is one of the most distinctive innovations of 20th century mathematics, can largely be traced back to her - in her published papers, lectures and her personal influence on her contemporaries. By now her contributions have become so thoroughly absorbed into our mathematical culture that only rarely are they specifically attributed to her. This book presents an extensive collection of her work. Albert Einstein wrote in a letter to the New York Times of May 1st, 1935: "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. In the realm of algebra, in which the most gifted mathematicians have been busy for centuries, she discovered methods which have proved of enormous importance in the development of the present-day younger generation of mathematicians."

Die Physik der Welterkenntnis

Auf dem Weg zum universellen Verstehen

Author: David Deutsch

Publisher: Springer-Verlag

ISBN: 3034860196

Category: Science

Page: 359

View: 4838

The Joy of x

Die Schönheit der Mathematik

Author: Steven Strogatz

Publisher: Kein & Aber AG

ISBN: 3036992693

Category: Mathematics

Page: 352

View: 5086

Mathematik durchdringt den ganzen Kosmos. Das weiß jeder, doch nur die wenigsten verstehen die Zusammenhänge wirklich. Steven Strogatz nimmt uns bei der Hand und spaziert mit uns durch diese Welt der Weisheit, Klarheit und Eleganz. Als Reiseleiter geht er neue, erfrischende Wege, deutet auf Besonderheiten, schildert Hintergründe und erklärt die unsichtbaren Mechanismen. Wir erfahren unter anderem von dem Wunder des Zählens, der genialen Einfachheit der Algebra, dem ewigen Erbe Newtons, dem Tango mit Quadraten, der Zweisamkeit von Primzahlen und der Macht des Unendlichen. Mit all seiner Begeisterung, seinem Scharfblick und seinem leichtem Ton hat Steven Strogatz ein herrliches Buch für alle geschrieben, die ihr Verständnis von Mathematik auf eine neue Art vertiefen möchten.

Bernhard Riemann 1826–1866

Wendepunkte in der Auffassung der Mathematik

Author: Detlef Laugwitz

Publisher: Springer-Verlag

ISBN: 3034889836

Category: Mathematics

Page: 348

View: 2177

Das Riemannsche Integral lernen schon die Schüler kennen, die Theorien der reellen und der komplexen Funktionen bauen auf wichtigen Begriffsbildungen und Sätzen Riemanns auf, die Riemannsche Geometrie ist für Einsteins Gravitationstheorie und ihre Erweiterungen unentbehrlich, und in der Zahlentheorie ist die berühmte Riemannsche Vermutung noch immer offen. Riemann und sein um fünf Jahre jüngerer Freund Richard Dedekind sahen sich als Schüler von Gauss und Dirichlet. Um die Mitte des 19. Jahrhunderts leiteten sie den Übergang zur "modernen Mathematik" ein, der eine in Analysis und Geometrie, der andere in der Algebra mit der Hinwendung zu Mengen und Strukturen. Dieses Buch ist der erste Versuch, Riemanns wissenschaftliches Werk unter einem einheitlichen Gesichtspunkt zusammenzufassend darzustellen. Riemann gilt als einer der Philosophen unter den Mathematikern. Er stellte das Denken in Begriffen neben die zuvor vorherrschende algorithmische Auffassung von der Mathematik, welche die Gegenstände der Untersuchung, in Formeln und Figuren, in Termumformungen und regelhaften Konstruktionen als die allein legitimen Methoden sah. David Hilbert hat als Riemanns Grundsatz herausgestellt, die Beweise nicht durch Rechnung, sondern lediglich durch Gedanken zu zwingen. Hermann Weyl sah als das Prinzip Riemanns in Mathematik und Physik, "die Welt als das erkenntnistheoretische Motiv..., die Welt aus ihrem Verhalten im un- endlich kleinen zu verstehen."

Symmetrien der Natur

Ein Handbuch zur Natur- und Wissenschaftsphilosophie

Author: Klaus Mainzer

Publisher: Walter de Gruyter

ISBN: 3110853655

Category: Philosophy

Page: 750

View: 7157

Gruppentheorie und ihre Anwendung auf die Quantenmechanik der Atomspektren

Author: Eugene Paul Wigner

Publisher: Springer-Verlag

ISBN: 3663025551

Category: Mathematics

Page: 332

View: 8406

Dieser Buchtitel ist Teil des Digitalisierungsprojekts Springer Book Archives mit Publikationen, die seit den Anfängen des Verlags von 1842 erschienen sind. Der Verlag stellt mit diesem Archiv Quellen für die historische wie auch die disziplingeschichtliche Forschung zur Verfügung, die jeweils im historischen Kontext betrachtet werden müssen. Dieser Titel erschien in der Zeit vor 1945 und wird daher in seiner zeittypischen politisch-ideologischen Ausrichtung vom Verlag nicht beworben.

Elementare Zahlentheorie

Author: Edmund Landau

Publisher: American Mathematical Soc.

ISBN: 0821836528

Category: Mathematics

Page: 180

View: 1572

Landau's monumental treatise is a virtual encyclopedia of number theory and is universally recognized as the standard work on the subject. The text is in German.

The heritage of Emmy Noether

Author: Mina Teicher

Publisher: N.A

ISBN: N.A

Category: Mathematics

Page: 101

View: 7054

Named for the noted mathematician, the Emmy Noether Research Institute for Mathematicsheld a two-day conference dedicated to her heritage and her influence on mathematics and physics in the 20th and 21st centuries. This volume presents the proceedings of that conference. It includes a comprehensive description of her contributions to commutative and noncommutative algebra, algebraic geometry, topology, and physics given by world experts in these fields. Also included is a profile of her life. The volume is a comprehensive collection of Noether's valuable contributions tomathematics and physics.