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Emmy Noether's Wonderful Theorem (Englisch) Taschenbuch – 7. Januar 2011

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  • Taschenbuch: 243 Seiten
  • Verlag: Johns Hopkins Univ Pr (7. Januar 2011)
  • Sprache: Englisch
  • ISBN-10: 0801896940
  • ISBN-13: 978-0801896941
  • Vom Hersteller empfohlenes Alter: Ab 18 Jahren
  • Größe und/oder Gewicht: 14 x 1,6 x 21,6 cm
  • Durchschnittliche Kundenbewertung: 3.0 von 5 Sternen  Alle Rezensionen anzeigen (2 Kundenrezensionen)
  • Amazon Bestseller-Rang: Nr. 74.848 in Fremdsprachige Bücher (Siehe Top 100 in Fremdsprachige Bücher)

Mehr über den Autor

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Neuenschwander writes well and gives thorough explanations. Choice 2011

Über den Autor und weitere Mitwirkende

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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12 von 12 Kunden fanden die folgende Rezension hilfreich Von HaraldK am 10. Juni 2012
Format: Taschenbuch Verifizierter Kauf
For some time already I was looking for a good introduction into the topic of Lagrangians, the Euler-Lagrange equations, the action integral and how they relate to symmetries and invariance. With a background more in mathematics than in physics, I found a few derivations that used too much physicist's math shortcuts that made it hard for me to follow.

This book has just the right mathematical rigor and detail to understand the derivations.
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0 von 13 Kunden fanden die folgende Rezension hilfreich Von Aki am 3. März 2014
Format: Taschenbuch
This book would be good for some one who isn't serious about theoretical physics, and just want to see how Noether's theory is like. Otherwise, it is better to study other things that are far more important such as Lie algebra.
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Die hilfreichsten Kundenrezensionen auf Amazon.com (beta)

Amazon.com: 17 Rezensionen
138 von 142 Kunden fanden die folgende Rezension hilfreich
A work of Art 27. Januar 2011
Von Charles W. Glover - Veröffentlicht auf Amazon.com
Format: Taschenbuch Verifizierter Kauf
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. Armed with the machinery from the first half of the book and the knowledge of what fields are, the author addresses the question of given gauge invariance what does Noether's theorem tell us about the properties of the Lagrangian.

Like most first addition books, there a few typos in the book but they are easy to spot and do not detract from the beautiful presentation of these subjects.

I hope you enjoy this as much as I did.
46 von 49 Kunden fanden die folgende Rezension hilfreich
long-needed celebration of the world's most important uncelebrated scientist delivers 26. Februar 2011
Von Gary - Veröffentlicht auf Amazon.com
Format: Gebundene Ausgabe
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.
35 von 37 Kunden fanden die folgende Rezension hilfreich
Would like to like it better 5. Dezember 2011
Von Henning Dekant - Veröffentlicht auf Amazon.com
Format: Taschenbuch Verifizierter Kauf
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.
8 von 8 Kunden fanden die folgende Rezension hilfreich
Very clear. 4. Dezember 2012
Von Alvaro Pastor - Veröffentlicht auf Amazon.com
Format: Taschenbuch Verifizierter Kauf
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.
7 von 8 Kunden fanden die folgende Rezension hilfreich
Near the top of the list of my favorite books ever 7. Februar 2014
Von readalot - Veröffentlicht auf Amazon.com
Format: Taschenbuch Verifizierter Kauf
I always wanted to know how physicists arrived at their results when they talk about (local and non-local) gauge theories, advanced ways of looking at Maxwell's equations, the covariant derivative, and how particles can be seen to have to satisfy certain requirements on their mass, to mention a few. I've read about these things in expository books like the excellent books by Frank Close. I am mostly self-taught in physics, other than having taken Physics I and II, classical dynamics and General Relativity. The General Relativity course was taken after I had read Steven Weinberg's excellent book on the subject on my own. I know that I have missed many of the small comments that a physics teacher would make during lectures. These small comments can add up to a deeper understanding and so I think I have missed that deeper understanding as well. This book makes me think I am being exposed to what I missed by not learning physics under a teacher at a school.

I could not stop reading this book. I admit that I did not do the problems right away but instead felt compelled to keep reading instead. I figured that I would read the book a few more times and do the problems some time later to really learn it. I even bought two versions of the book. The first version was a paperback and the second was the Kindle book so that I could go back to the book and study it whenever I was near a computer. I have never bought two versions of a book before this.

Before I bought the book, I worried about a couple of reviews, which pointed out some errors. One such review mentioned the incorrect statement of a theorem having to do with the result that the Euler-Lagrange equation describes a function that would minimize an integral. I would swap this minor lapse any day for the clarity of Neuenschwander's presentation. There are many books on the calculus of variations that would state the theorem flawlessly yet would remain devoid of any clarity and motivation. I would classify Neuenschwander's misstatement of the theorem as a typo.

A couple of cool features:

Neuenschwander has a section in which he physically motivates the minus sign in K - U of Hamilton's principle. I bet that this section answers a question that has occurred to everyone dealing with both the Lagrangian and the Hamiltonian. The only other author I remember mentioning anything about the minus sign was John Baez in online student notes of his classical dynamics class. (I wish Neuenschwander would write another book about the physical significance of the Euler-Lagrange equation beyond the standard context of it being used as a tool in variational calculus.)

There's even an appendix which discusses the Legendre transformation and helps one see that there's way more to the correspondence between the Lagrangian and Hamiltonian than a trivial change between variables v and p and a trivial sign change from + to -.

I closely read all the appendices and found them worthwhile.

I like watching great physicists lecture on YouTube. I have really gained a lot by listening to Susskind speak on a whole range of topics. I have watched old lectures by Dirac, which are unbelievably good. I have really enjoyed lectures given by 't Hooft. There are many good expositors on YouTube as well. For instance, I have watched drphysicsA and doctorphys.

I wish that Dwight Neuenschwander would start doing YouTube lectures or maybe teach a course for the Great Courses at the Learning Company. I'm sure that he would have a large and appreciative audience.
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