Emmy Noether's Wonderful Theorem

Name: Emmy Noether's Wonderful Theorem
Brand: JOHNS HOPKINS UNIVERSITY PRESS
Price: 68.99 AUD
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By: Dwight E. Neuenschwander

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Paperback | 27 May 2011

At a Glance

Paperback
264 Pages

Age
18+

Dimensions(cm)
21.59 x 13.97 x 2.54

New Edition

Published: 14th June 2017

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A beautiful piece of mathematics, Noether's Theorem touches on every aspect of physics. Emmy Noether proved her theorem in 1915 and published it in 1918. This profound concept demonstrates the connection between conservation laws and symmetries. For instance, the theorem shows that a system invariant under translations of time, space, or rotation will obey the laws of conservation of energy, linear momentum, or angular momentum, respectively. This exciting result offers a rich unifying principle for all of physics.

Dwight E. Neuenschwander's introduction to the theorem's genesis, applications, and consequences artfully unpacks its universal importance and unsurpassed elegance. Drawing from over thirty years of teaching the subject, Neuenschwander uses mechanics, optics,geometry, and field theory to point the way to a deep understanding of Noether's Theorem. The three sections provide a step-by-step, simple approach to the less-complex concepts surrounding the theorem, in turn instilling the knowledge and confidence needed to grasp the full wonder it encompasses. Illustrations and worked examples throughout each chapter serve as signposts on the way to this apex of physics.

Noether's Theorem is an essential principle of post-introductory physics. This handy guide includes end-of-chapter questions for review and appendixes detailing key related physics concepts for further study.

Industry Reviews

Neuenschwander writes well and gives thorough explanations. Choice Without entering into technicalities, the author nevertheless succeeds in preserving a reasonable standard of mathematical rigor and, above all, in convincing the reader of the mathematical beauty and physical relevance of Noether's theorem. If only for that reason, I can strongly recommend this book. -- Frans Cantrijn Mathematical Reviews A very readable and concrete introduction to symmetry and invariance in physics with Noether's (first) theorem providing a unifying theme... The style of writing is very engaging and conveys the enthusiasm of the author... The book contains many interesting examples as well as excellent exercises. -- James Vickers London Mathematical Society Newsletter

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You Can Find This Book In

Non-Fiction Science Physics Mathematics Applied Mathematics Miscellaneous Items History of Mathematics

Preface	p. xi
Acknowledgments	p. xiii
Glossary of Symbols	p. xv
Primary and Auxiliary Questions	p. xvii
Prologue	p. 1
Symmetry, Invariance, and Conservation Laws	p. 1
Emmy Noether Biographical Notes	p. 6
When Functionals Are Extremal
Functionals	p. 15
Single-Integral Functionals	p. 15
Formal Definition of a Functional	p. 20
Extremals	p. 25
The Euler-Lagrange Equation	p. 25
Corollaries to the Euler-Lagrange Equation	p. 31
On the Equivalence of Hamilton's Principle and Newton's Second Law	p. 36
Where Did Hamilton's Principle Come From?	p. 39
Why Kinetic Minus Potential Energy?	p. 47
Extremals with External Constraints	p. 49
When Functionals Are Invariant
Invariance	p. 61
Formal Definition of Invariance	p. 61
Condition for Invariance: The Rund-Trautman Identity	p. 66
A More Liberal Definition of Invariance	p. 68
Emmy Noether's Elegant Theorem	p. 72
Extremal + Invariance = Noether's Theorem	p. 72
The Inverse Problem: Finding Invariances	p. 75
Adiabatic Invariance and Noether's Theorem	p. 79
The Invariance of Fields
Fields and Noether's Theorem	p. 91
Multiple-Integral Functionals	p. 91
Euler-Lagrange Equations for Fields	p. 96
Canonical Momenta and the Hamiltonian for Fields	p. 99
Equations of Continuity	p. 101
The Rund-Trautman Identity for Fields	p. 103
Noether's Theorem for Fields	p. 107
Complex Fields	p. 108
Global Gauge Transformations	p. 113
Gauge Invariance as a Dynamical Principle	p. 125
Local Gauge Invariance and the Covariant Derivative	p. 125
Electrodynamics as a Gauge Theory I: Field Tensors	p. 129
Pure Electrodynamics, Spacetime Invariances, and Conservation Laws	p. 135
Electrodynamics as a Gauge Theory II: Sources and Minimal Coupling	p. 140
Internal Degrees of Freedom	p. 143
Non-Abelian Gauge Transformations	p. 153
Post-Noether Invariance
Invariance in Phase Space	p. 171
Phase Space	p. 171
Hamilton's Principle in Phase Space	p. 172
Noether's Theorem through Hamilton's Equations	p. 175
Hamilton-Jacobi Theory	p. 177
The Action as a Generator	p. 191
Conservation of Probability and Unitary Transformations	p. 192
Continuous Spacetime Transformations in Quantum Mechanics	p. 195
Epilogue	p. 200
Appendixes
Scalars, Vectors, Tensors, and Coordinate Transformations	p. 205
Special Relativity	p. 211
Equations of Motion in Quantum Mechanics	p. 217
Legendre Transformations and Conjugate Variables	p. 221
The Jacobian	p. 225
Bibliography	p. 229
Index	p. 235
Table of Contents provided by Ingram. All Rights Reserved.

Emmy Noether's Wonderful Theorem

At a Glance

New Edition

Paperback

Industry Reviews

Shipping

How to return your order

Defective items

You Can Find This Book In

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