Physics From Symmetry

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  • #26
haushofer
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See also the recent beautiful insight about how to obtain GR from Poincare symmetries :P
 
  • #27
strangerep
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I have asked the library at my institution to buy it. Hope I didn't make a mistake :nb)
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 [:oldwink:] :- 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.
 
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  • #28
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OT, does anyone have a link to an intro level explanation of Noether's theorem.
 
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  • #32
dextercioby
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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.
 
  • #33
strangerep
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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.
Well, the Kepler problem is classical, last time I checked. :-p

The author definitely tried to address a certain amount of QM and QFT -- see chapters 5,8,9.
 
  • #34
Demystifier
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I apply a "test" to any physics book
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.
 
  • #35
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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
 
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  • #36
Demystifier
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The author is a kid and that says it all.
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.
 
  • #37
dextercioby
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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. [...]
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.
 
  • #38
Demystifier
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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.
 
  • #39
dextercioby
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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.
 
  • #40
Demystifier
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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?
 
  • #41
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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?
I have now gone through the book.

It has technical errors, but gee so do other textbooks I read - its in fact a good exercise picking them up. It is also too cumbersome in places - I can find more elegant explanations to replace some of the long calculations he does.

But actually wrong - not so sure about that. Its advantage is exactly what I said. A professor that posts here has said, and IMHO its totally true as far as reactions go - it was mine when I learnt about it and had a very deep effect on me - when he teaches Noether's Theorem there is stunned silence as its import sinks in. This whole book is built around that famous theorem at a level 2-3 year undergrads would understand. It contains nothing new - but being exposed to exactly why the Higgs theoretically was thought to exist and other areas not usually at the undergrad level is very uplifting. And for many that genuinely likes theoretical physics seeing the importance of symmetry early on is - well uplifting.

It's like Landau - Mechanics. It contains nothing new - but is presented in such a brilliant, different and concise manner you sit in awe - all physicists should study it. Of course this guy is nowhere in Landau's class but like Landaus book, its different perspective is so inspiring.

Thanks
Bill
 
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  • #42
vanhees71
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That's really ridiculous. The book was written very early in the history of relativity (15 years from Einstein's SR paper and just 5 years from the final formulation of GR), and not only given that it's very good. It's written by a physicist, and that it is not overwhelmingly differential geometrical is rather a good than a bad point. The only thing, I'd consider outdated in this book is the treatment of thermodynamics. Nowadays we consider temperature and chemical potential to be scalars, and that's how these quantities should be considered, but these issues were settled in the 1960ies only. Otherwise you can pretty well use this book to learn about SR and GR from it even nearly 100 years later!

Another masterpiece of Pauli's is the book on quantum mechanics. Although from the 1930ies it's astonishingly up to date.
 
  • #43
vanhees71
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I have now gone through the book.

It has technical errors, but gee so do other textbooks I read - its in fact a good exercise picking them up. It is also too cumbersome in places - I can find more elegant explanations to replace some of the long calculations he does.
Bill
I don't know, what you mean. It's been some time I've looked into Pauli's relativity book, but I cannot remember that I found any technical errors. Can you point specifically to some? I wish more textbooks today had the quality of Pauli's book!
 
  • #44
Demystifier
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I don't know, what you mean. It's been some time I've looked into Pauli's relativity book, but I cannot remember that I found any technical errors. Can you point specifically to some? I wish more textbooks today had the quality of Pauli's book!
That was not about the Pauli's book.
 
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  • #45
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That was not about the Pauli's book.
No it wasn't. Its not even approaching the class of those all time classics.

It's far from perfect. Why I like is it is a different take on physics not usually presented at the level of its intended audience ie the importance of symmetry unifying all of physics. It was written by a 22 yo masters degree candidate so don't expect anything earth shattering. Guys like Pauli etc are very very rare and this guy is no Pauli.

If you like it as I do - great - if you don't - that's great as well. Its just different.

We have a number of professors that post here - they may or may not use it in their classes, but what I can say for sure is the ideas it presents would have been of great value to me if I was taught it second or third year of my degree. So maybe, perhaps not using this book, something along those line could be done.

Another similar book at that level, although it doesn't cover as much material, is:
https://www.amazon.com/dp/0801896940/?tag=pfamazon01-20

I have a copy - and really like it as well.

Have a look at:

She wanted to be a writer. But after being exposed to Noether saw the real beauty of physics. Want more people to study physics? Expose them to these ideas early on. That's why I like these books - physics real beauty can be taught a bit earlier than is usually done. I don't mean hand-wavy pseudo science - but the real deal. These ideas were life changing for me, for the girl in the video and if exposed to it I suspect for many others. She wanted to be a writer - me applied math - but physics real essence and beauty had me hooked once I understood it.

Thanks
Bill
 
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