Overview

""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.

Full Product Details

Author:   Dwight E. Neuenschwander (Professor of Physics, Department Chair, Southern Nazarene University)
Publisher:   Johns Hopkins University Press
Imprint:   Johns Hopkins University Press
Edition:   revised and updated edition
Dimensions:   Width: 15.20cm , Height: 2.10cm , Length: 22.90cm
Weight:   0.454kg
ISBN:  

9781421422671

ISBN 10:   1421422670
Pages:   344
Publication Date:   27 May 2017
Audience:   College/higher education ,  Tertiary & Higher Education
Format:   Paperback
Publisher's Status:   Active
Availability:   Available To Order  
We have confirmation that this item is in stock with the supplier. It will be ordered in for you and dispatched immediately.

Table of Contents

"Preface Acknowledgments Questions Part I. When Functionals Are External 1. Symmetry 1.1. Symmetry, Invariances, and Conservation Laws 1.2. Meet Emmy Noether 2. Functionals 2.1. Single-Integral Functionals 2.2. Formal Definition of a Functional 3. Extremals 3.1. The Euler-Lagrange Equation 3.2. Conservation Laws as Corollariesto the Euler-Lagrange Equation 3.3. On the Equivalence of Hamilton's Principleand Newton's Second Law 3.4. Where Do Functional Extremal PrinciplesCome From? 3.5. Why Kinetic Minus Potential Energy? 3.6. Extremals with External Constraints Part II. When Functionals Are Invariant 4. Invariance 4.1. Formal Definition of Invariance 4.2. The Invariance Identity 4.3. A More Liberal Definition of Invariance 5. Emmy Noether's Elegant (First) Theorem 5.1. Invariance + Extremal = Noether's Theorem 5.2. Executive Summary of Noether's Theorem 5.3. ""Extremal"" or ""Stationary""? 5.4. An Inverse Problem 5.5. Adiabatic Invariance in Noether's Theorem Part III. The Invariance of Fields 6. Noether's Theorem and Fields 6.1. Multiple-Integral Functionals 6.2. Euler-Lagrange Equations for Fields 6.3. Canonical Momentum and the HamiltonianTensor for Fields 6.4. Equations of Continuity 6.5. The Invariance Identity for Fields 6.6. Noether's Theorem for Fields 6.7. Complex Fields 6.8. Global Gauge Transformations 7. Local Gauge Transformations of Fields 7.1. Local Gauge Invariance and Minimal Coupling 7.2. Electrodynamics as a Gauge Theory,Part 1 7.3. Pure Electrodynamics, Spacetime Invariances,and Conservation Laws 7.4. Electrodynamics as a Gauge Theory,Part 2 7.5. Local Gauge Invariance and Noether Currents 7.6. Internal Degrees of Freedom 7.7. Noether's Theorem and GaugedInternal Symmetries 8. Emmy Noether's Elegant (Second) Theorem 8.1. Two Noether Theorems 8.2. Noether's Second Theorem 8.3. Parametric Invariance 8.4. Free Fall in a Gravitational Field 8.5. The Gravitational Field Equations 8.6. The Functionals of General Relativity 8.7. Gauge Transformations on Spacetime 8.8. Noether's Resolution of an Enigma inGeneral Relativity Part IV. Trans-Noether Invariance 9. Invariance in Phase Space 9.1. Phase Space 9.2. Hamilton's Principle in Phase Space 9.3. Noether's Theorem and Hamilton's Equations 9.4. Hamilton-Jacobi Theory 10. The Action as a Generator 10.1. Conservation of Probabilityand Continuous Transformations 10.2. The Poetry of Nature Appendixes A. Scalars, Vectors, and Tensors B. Special Relativity C. Equations of Motion in Quantum Mechanics D. Conjugate Variables and Legendre Transformations E. The Jacobian F. The Covariant Derivative Bibliography Index"

Reviews

Neuenschwander displays the instincts of a good teacher and writes clearly. Using Noether's Theorem as an overarching principle across areas of theoretical physics, he helps students gain a more integrated picture of what sometimes seem to be independent courses--an ever-important thing for undergraduate physics education.</p>--Cliff Chancey, University of Northern Iowa

Author Information

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.

Tab Content 6

Author Website:  

Customer Reviews

Recent Reviews

No review item found!

Add your own review!

Countries Available

All regions