Actually Ballentine did it better but didn't mention that was what he was doing. This guy explicitly did, as well as carefully analysing Noethers theorem which Ballentine did not. Ballentine also introduces the Born rule formalism prior to doing it - this book uses it to motivate it. Different intent and emphasis. Ballaintine is the much better book to learn QM from - this book motivates the importance of symmetry as a unifying concept in physics.

The professor thing doesn't really worry me - he is trying something different - maybe too different for more set in their ways professors.

Read the paper I linked to on relativity. An inertial frame is defined by symmetry proprieties and that is all you need to derive the Lorentz transformations.

The first, unlike this book, doesn't eve mention group theory or Noethers theorem. You see mechanics developed directly from symmetry. For example from the fact the Lagrangian must be invariant between inertial frames we see mass must exist and be positive.

Then we have Noethers theorem itself which says (loosely) for every symmetry in the Lagrangian their must be a conserved quantity. Its why momentum exists and is conserved (systems have the same Lagrangian where you put them is the conserved quantity associated with this and is called momentum) and energy exists and is conserved (systems often have Lagrangian's that are time invariant which has the conserved quantity we call energy). Noether proved it must be the case. It shocked even Einstein and just about anyone else exposed to it since then. It explains why defining energy in GR is a BIG problem - but you should take that over to the GR forum.

This book is different, I would not have done it in this order but starts with group theory and Noethers theorem then develops the physics. Its a very different and unusual approach as you can see some do not like. I do - but that's just me. Time will tell if the method takes off or not. From comments by actual professors here I may be its only advocate - maybe it needs to be done by an experienced teacher and textbook writer.

The answer is Nothers threroem.

You usually learn mechanics, EM, QM etc etc then this beautiful theorem. This book does the reverse.

Once understood its shocking. Professors here often describe the stunned silence of their students when they teach it. Its that deep and profound. This book is an attempt to do the reverse - but as you can see many do not warm to that approach like I do. They all recognise the power, beauty and usefulness of Noether and are as shocked by it now just like when they learned it. But starting from it - well obviously that is not universally as well respected.

Well, if you ever have written a longer scientific text, you'd know how easily typos sneak into a manuscript, and it is not easy to get them when you just have typed a text in, because you read over them knowing your text very well. Waiting a few months and then proofreading helps.

On the other hand you are right in being angry with the publishers. Nowadays the publishers have no serious editing anymore. That's indeed something you can blame them on since they really take a lot of money for their books.

At the risk of being a wet blanket, I think you should try to stop that purchase until you've had a chance to examine at least parts of the book for yourself. I'll send you a PM shortly.

I just had a quick skim and I will say that I was underwhelmed.

I apply a "test" to any physics book that waxes lyrical about the wonders of symmetries [] :- I look for how it develops the Kepler laws, especially the 3rd law. The latter arises from a symmetry which is not connected to a Noetherian conserved quantity. Thus, it reminds us that not everything follows from an algebra of conserved quantities, but rather from the full dynamical group that maps solutions of the equations of motion among themselves. Noetherian symmetries, although very important, are nevertheless not the be-all and end-all of everything.

Schwichtenberg does not mention Kepler at all, afaict. Nor does he mention "hydrogen" which is a marvelous example of the power of group theory in QM.

Further, when I look at his derivation of the half-integer spectrum for su(2), there's some leaps in there that I don't like. Look at sect 3.6.1 on pp 53-54. He introduces ladder operators ##J_\pm## and shows that they act on ##J_3## eigenvectors to raise/lower the eigenvalue. Then he concludes that, because he's working in a finite dimensional space, there must be a point where repeated application of ##J_\pm## yields 0. Although this is technically correct, (because his space happens to also be a Hilbert space, and eigenvectors of a Hermitian operator with distinct eigenvalues are orthogonal, and span the space according to the spectral thm), but he doesn't explain any of this. It works out because he's working with SU(2), hence unitarity is there automatically, and hence also Hermiticity of its generators (see sect 3.4.3).

Contrast this with the treatment in Ballentine sect 7.1. There's no comparison, imho.

It's also disappointing that he hasn't enabled the "Look Inside" feature on Amazon. That makes it hard for people to get a feel of the book for themselves before committing their money.

Strangerep, there's no mentioning of the Kepler problem and its symmetries (dynamical group SO(2,4) etc), because the focus of the book is on classical field theory, not on quantum mechanics. The quantum field symmetries (Ward-Takahashi, BRST, anomalies, gauge symmetry breaking) are not mentioned at all, because the book is meant for undergraduates (heck, the author was undergraduate at the time of writing the book!), hence it should be and it is full of the blah-blah of standard texts. You are right to complain about the treatment of the su(2) - angular momentum part, simply because the whole picture (compact group - Peter-Weyl theorem-unitary ray representations of SO(3)-Bargmann's theorems - Nelson's theorem) is not clear to the author himself.

My main criteria for reading a new book on old subject is - does it offer a new perspective? (Otherwise, what's the point of either writing or reading it in the first place?) And I think this book definitely satisfies this criterion.

Schwichtenberg's book is quite good. I especially liked the chapter on Lie groups, whose treatment of representation theory was exceptionally clear. Another book that is in much the same vein as Schwichtenberg's, but at a somewhat more advanced level, is Kurt Sundermeyer's 'Symmetries in Fundamental Physics' (disregard the one-star review--the reviewer apparently confused Schwichtenberg's book for Sundermeyer's): https://goo.gl/oFE3ky

Well, Pauli was also a kid when he has written a book on relativity (both special and general). Yet, it is still considered one of the best books on relativity ever written.

Speaking of kids, Wolfram, the creator of Mathematica, has written a review of weak interactions in particle physics when he was a kid. This review can be found by google, but I cannot tell how good it is.

He was 20 when he wrote it and 21 when published. It was the first monograph on General Relativity (appeared in the same year with the one by Max von Laue) and it is very good, even though it is written with no differential geometry content. But you can't expect that any physics undergraduate in Germany being offered the chance of a lifetime (i.e. publish a book on science at Springer Verlag) turn out to be a prodigy and a future Nobel Prize winner.

OK, fair enough, but answer this one. If the book is so bad, why do so many people (on this forum at least) find the book very good? There must be something about that book that looks appealing and I would like to know what that something is.

Don't ask me, I find it appalling that books get passed an editor's proofreading. It is ridiculous to ask a 22 yo to write a book then publish it with 100 errors in it.
The material in this book is found in a dozen other books, but I presume it's the relatively low level of mathematics that is a magnet for some readers.

You have mentioned that errors are not only technical (which are probably easy to fix), but also conceptual. Can you pinpoint to some of the conceptual errors?