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Emmy Noether's Wonderful Theorem Hardcover – November 16, 2010

ISBN-13: 978-0801896934 ISBN-10: 0801896932 Edition: 1st

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Product Details

  • Hardcover: 264 pages
  • Publisher: Johns Hopkins University Press; 1 edition (November 16, 2010)
  • Language: English
  • ISBN-10: 0801896932
  • ISBN-13: 978-0801896934
  • Product Dimensions: 5.5 x 0.9 x 8.5 inches
  • Shipping Weight: 12.8 ounces (View shipping rates and policies)
  • Average Customer Review: 4.1 out of 5 stars  See all reviews (16 customer reviews)
  • Amazon Best Sellers Rank: #2,603,451 in Books (See Top 100 in Books)

Editorial Reviews

Review

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.

(Dr. Cliff Chancey, University of Northern Iowa)

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)

About the Author

Dwight E. Neuenschwander is a professor of physics at Southern Nazarene University and editor of the Society of Physics Students Publications of the American Institute of Physics. He won the Excellence in Undergraduate Physics Teaching Award from the American Association of Physics Teachers.


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Customer Reviews

I've read about these things in expository books like the excellent books by Frank Close.
readalot
The type of person who buys this book will probably sit down and go through the derivations and verify them (or spot the glitch as the case may be).
Peter Haggstrom
In the last half of the book, the author teaches you how Noether's theorem is used in quantum field theory.
Charles W. Glover

Most Helpful Customer Reviews

136 of 140 people found the following review helpful By Charles W. Glover on January 26, 2011
Format: Paperback Verified Purchase
I am a lifelong student of Physics. I have been a student long beforeI got my PhD in Physics. I am currently a Distinguished Scientist at a Government Lab. This is first review (and possibly the last) I've written for an Amazon book, but I felt compelled to write this after reading this book. It is an excellent example of a 'true' teacher at work who understands how to relate information. This is an art form.

In this book you will learn about Emmy Noether and her work in relating a huge class of conservation laws to nature's symmetries. The book explores how symmetry, invariance and conserved quantities are related, quantitatively. The first half of the book is written for self-study by an undergrad Physics student. It deals predominately with functionals (what are they), functional extremals, and when they are invariant. These chapters are the prelude to Noether's Theorem and Rund-Trautman's version of the theorem. This work first inquires whether a functional is invariant under a given transformation, and if it is, it uses Noether's theorem to get the associated conservation law. Next, it examines the inverse problem; given the transformation can you seek the Lagrangian whose functionals are invariant. In each section the author works examples in some detail and carries these examples with further detail in each of the following chapters. It's like a novel for physicists.

In the last half of the book, the author teaches you how Noether's theorem is used in quantum field theory. He describes the concept of a field through simple examples and introduces Lagrangian densities. Then Noether's theorem is developed for fields and, in particular, quantum fields.
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45 of 48 people found the following review helpful By Gary on February 26, 2011
Format: Hardcover
About half-way through, but I already appreciate the biographical information about Noether, and the overview and applications of her results to a variety of problems. The mathematical level is appropriate for upper level undergraduate physics majors and the discussion really helps place the results in context. Nice problems and thought-provoking comments at the end of each chapter. Could use more graphics, and perhaps a little more prose to address the formal mathematical subtleties, but overall, this book admirably fills the largest hole in that small bookshelf containing useful celebrations of deeply significant science and the scientists who created it.
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34 of 36 people found the following review helpful By Henning Dekant on December 4, 2011
Format: Paperback Verified Purchase
This book addresses an important gap in the landscape of textbooks on theoretical mechanics. I strongly feel this is the way the subject should be approached as Noether's theorem has such far reaching implications beyond just classical mechanics.

Yet, there are annoying glitches. E.g. the oversight on p.28 with regards to the fundamental lemma of the calculus of variations as has been pointed out in a previous review.

On page 99 the equation (6.3.1) for the Hamiltonian density is incorrect. The way it is written the first term sums over all coordinate indexes. Correct would be to only have time i.e. index zero appear in the first term and sum over all field components if we deal with more than a simple scalar field.

Other times the authors just presents an equation without a modicum of information of how we got there. I.e. the alternative form of the Rund-Trautman identity (RTI II) is given on p.68. It's easy enough to see how the right side follows from RTI I when substituting the canonical variables and using the product rule, but how does the left side of RTI II come about? How does the Euler-Lagrange identity reappear there? (I attached a comment to this review if you are looking for the answer).

Still, I enjoy the book but I would have liked to like it even better.
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7 of 7 people found the following review helpful By Alvaro Pastor on December 3, 2012
Format: Paperback Verified Purchase
Neuenschwander's superb explanation of Lagrangian and Hamiltonian mechanics will lead you to the best introduction to Noether's theorem I have read.
This well written book is graspable by anyone with multivariate calculus knowledge.
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75 of 103 people found the following review helpful By A techno geek on July 3, 2011
Format: Paperback
O.k. help me with this. On p. 28 the author writes (sorry if the math code is hard to read here):

"Lemma (Fundamental Lemma of the Calculus of Variations):
If n(t) is not identically zero in \int_a^b A(t) n(t) dt = 0,
where n(a)=n(b)=0, and
if on the closed interval [a,b] both A(t) and n(t) are twice differentiable,
then A(t) = 0 throughout [a,b]."

This is obviously not true, as seen in the following counterexample:
Let n(t) = sin( 2 pi (t-a)/(b-a) ), and A(t) = 1.
So, n(t) satisfies the stated constraints, and \int_a^b A(t) n(t) dt = \int_a^b sin( 2 pi (t-a)/(b-a) ) dt = 0, yet A(t)=1 is most certainly not 0.

What in the world? Consultation of other author's expositions (e.g. Weinstock's Calculus of Variations or Gelfand and Fomin's Calculus of Variations) reveals that Neuenschwander left out the most crucial phrase in his version of the lemma: "If for EVERY choice of the continuously differentiable function n(t) ..."

How could he be so sloppy in something as fundamental as the Fundamental Lemma of the Calculus of Variations? (I am tempted to make a physicist joke here but I won't).

Once one encounters an error this egregious --- and only on p. 28 --- how can one trust that the author is a faithful guide to this new territory?

And now my mind starts to wonder about other things in the book. I recall the discomfort I felt back on p. 20:

"2.2 Formal Definition of a Functional.
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