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Emmy Noether's Wonderful Theorem
Download Emmy Noether's Wonderful Theorem
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Review
"As this book is well written and contains a very good set of exercises, it can serve as the primary text for a special topics course." (Choice)"Nadis gives no technical details, but Neuenschwander does, in a book for physics majors with a strong background in mathematics; the book does not shy away from Lie groups and the study of invariants. This new edition delves into distinctions between two Noether theorems and adds more exercises, references, and details." (Mathematics Magazine)"Neuenschwander sets out from the beginning to help the reader who must be familiar with calculus and a few other standard topics, but who is not yet fluent in these areas... His role is to be the teacher on the side, prompting the reader with interesting observations and questions... He anticipates problems, guides you yet also makes you think things through... Not only a very worthwhile read for its content but also for its style." (Ken Zetie, St. Paul's School Mathematical Gazette)"Well-written... Throughout there is reference to the life of Emmy Noether, including the many difficulties related to being a woman in a man's world... I am glad her story is given an airing here as she fails to be as famous as she undoubtedly should be." (Phil Dyke, FIMA Mathematics Today)"Technical and yet ultimately poetic book on Emmy Neother's wonderful theorems... Neuenschwander's work is recommended for anyone who wants to gain a deeper understanding and appreciation of the physics and mathematics behind Emmy Noether's work, as well as the particular challenges she faced in her life." (Miriam R. Aczel, Centre for Environmental Policy, Imperial College London Contemporary Physics)
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Review
"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." (London Mathematical Society Newsletter)"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." (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." (Mathematical Reviews)
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Product details
Paperback: 344 pages
Publisher: Johns Hopkins University Press; revised and updated edition edition (April 1, 2017)
Language: English
ISBN-10: 1421422670
ISBN-13: 978-1421422671
Product Dimensions:
6 x 0.8 x 9 inches
Shipping Weight: 15.5 ounces (View shipping rates and policies)
Average Customer Review:
4.4 out of 5 stars
29 customer reviews
Amazon Best Sellers Rank:
#672,646 in Books (See Top 100 in Books)
I love this book! It isn't an easy read but if you are willing to spend the time to read it thoroughly (for me that meant reading it from cover to cover over 7 times before I felt I had a reasonable understanding of the subject) you will understand why Einstein and others of his generation considered Dr. Noether to be one of the greatest mathematicians during the early years of the 20th century. I have a reasonable math background (a B.S. in Applied Mathematics) which was a real help with the subject matter of the book. If you are an upper division math or physics major you should be able to understand the importance of Noether's work. Dr. Neuenschwander does a good job of organizing and presenting the material.
Pedagogic physics starts with specific non-provable rules and derives mathematical statements that lead into mechanics, fields, optics, etc.These rules include the conservation of energy, momentum, etc. This little gem of a book lays the foundation to understand Emmy Noether's work to try to reverse that understanding to state the Lagrangian or Hamiltonian and then if you can establish symmetry then you can prove those assumed rules. The mathematics is beautiful, but the philosophy is not so firmly established. Instead you may have a tautology where the Hamiltonian is just another statement of the conservation law that you are trying to prove. The foundations of the math itself are not independent of assumption. Frankly, I was delighted to find that I could read and comprehend the level of mathematics presented in this book. For me, the most important point was that conservation laws depend upon symmetry or more simply they have qualifying statements. Thus the evolution of physics is really trying to understand the qualifying statements and the logic that variations imply. Thus, we are not stuck with the "Ten Commandments of Physics" but we may strive to find and establish new and more comprehensive rules about the way things work. By all means, read this book.
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.
The author states "The reader I have in mind is a junior or senior under graduate physics student, or a beginning physics graduate student. Well do I remember being one of those students myself. Those memories include the frustration of trying to read a manuscript loaded with jargon that assumed a fluency I was still struggling to master. At that point in one's career, details that are incidental trifles to experts can become major sticking points for novices (see the following list of questions for example)." This quote comes from page XI, on page XV and XVI is the list of PRIMARY and AUXILLARY QUESTIONS which he leaves to "us" to discover the answers too. The other thing the author states is before we read this book we should get hold of Emmy Noether's original paper, which the author could have given us in the book (it is public domain). Once you get through this book with understanding of the subject you will be able to write a better explanation of the theorem.
References to the Noether's theorem are aplenty in modern physics books, with various levels of depth depending on a specific usage. This book is special in focusing on the theorem itself and in providing all necessary conceptual environment for complete understanding of its meaning, sources, consequences, and limitations. I enjoyed clear explanations with careful attention to subtle details.
The author does a great service by providing a readable gateway text into mathematical physics.This is the second edition of this wonderful book. I worked through the 1st edition and was delayed by some errors. So far, all the errors that delayed me in the 1st edition have been fixed.Having said this, the author has taken a few worked examples and made them into homework problems. The autodidactic reader may not find this as helpful as worked examples.
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