Other What Undervalued Books Have You Discovered?

[kith]

Not really undervalued in comparison to similar books but I know many phycicists who've never read a single book on its topic:
John Taylor - Introduction to Error Analysis

 

[vanhees71]

Yes - he wanted to take the "square root" of the Klein-Gordon equation - I think everything he did initially was imagining relativistic QM - although that didn't work, and eventually he and others understood that it really has to be understood as a many-body equation. Yes, not undervalued, just replaying to your comments on relativistic QM, with which I agree - except that I think one has to mention it for at least 5 second to explain why we still have this term called "second quantization".

Of course, Dirac had to "invent" the thing. The first relativistic wave equation written down was, no surprise, the Klein-Gordon equation, but that's a misnomer, because it was Schrödinger who tried this equation first. In solving the hydrogen problem he realized that he got the wrong fine structure which was already known to be due to relativity from oldfashioned Bohr-Sommerfeld quantization, which by chance gives the correct fine structure. Then he went a step back and thought about non-relativistic wave mechanics and published his paper series on "Quantization as an eigenvalue problem".

Dirac then realized that indeed the Klein-Gordon equation lacks the spin to describe an electron, and he thought about particles with spin 1/2. At the same time he thought he can solve the problem with the negative-frequency solutions (falsely interpreted as negative-energy solutions) by choosing only the positive sqaure root of the relativistic energy-momentum relation $E^2-\vec{p}^2=m^2$ (using $c=\hbar=1$), i.e., $E=+\sqrt{\vec{p}^2+m^2}$. He also knew that just taking the square root in an operator sense is "dangerous" and thus he came to the discovery of the Clifford-algebra ansatz, i.e., the Dirac matrices and their realization as a four-dimensional spinor. What's behind it, is of course the representation theory of the Poincare group underlying all relativistic physics, which was revealed by Weyl and Wigner a bit later.

Anyway, Dirac quickly realized that his trick doesn't work for interacting particles. For the hydrogen atom however it works, since the interaction is weak and the bound-state problem is close to a non-relativistic limit. In this way the Dirac equation leads to the correct fine structure of the hydrogen spectrum. However, it was soon realized that in general this cannot be the right way to construct a relativistic quantum mechanics, because whenever relativity becomes really relevant (and not only for small corrections to the non-relativistic limit) you run into trouble, because the negative-frequency modes cannot be neglected. Now Dirac's next ingeneous idea comes in. His idea was to redefine the ground state such that all negative-frequency states are occupied with electrons. At this point the argumentation becomes inconsistent, because you pretend you could use a single-particle approach and then by hand introduce a quite problematic state of infinitely many particles present in the ground state. Of course, you can argue that you can redefine the infinite energy by subtracting an infinite constant, but what about the infinite amount of negative charge? But Dirac went on and declared that the ground state, including his "sea" occupying the negative-frequency (here interpreted as negative-energy) states has 0 energy and 0 electric charge. Then he concluded further, and that's now very clever again, that the problems with the interacting Dirac particles are solved in interpreting that transitions of an electron from the sea into the postive-frequency domain means nothing else than the creation of a hole, which effecitvely occurs phenomenolgically as a positive charge. In disfavour of introducing new particles (which was not appreciated in the late 1920ies) he first tried to interpret the holes in his sea as protons, but he was soon corrected by Oppenheimer that his holes must represent particles of the same mass as electrons, and this lead finally to the prediction of antielectrons (soon named positrons). Later on Dirac worked out a complete version of QED from his "hole theory", and in fact it is pretty much the same theory that also comes out within the modern QFT formulation, but it's unnecessarily complicated and pretty inconsistent even in the heuristics to "derive" it. That's why I think it's better to teach relativistic QT as relativistic QFT right away from the very beginning. With a good basis of non-relativistic QM and "2nd quantization", which is nothing else than non-relativistic QFT for many-body systems admitting also the production and destruction of particles (in applications of non-relativistic QFT that applies of course not to the "real" particles but to a whole zoo of quasiparticles in condensed-matter systems, but that's another story).

 

[Aufbauwerk 2045]

Dimensional Analysis by P. W. Bridgman. Even among those who have heard of it, how many have actually read it? It is not a trivial subject as some may think. It's well worth the time, as is Bridgman's The Logic of Modern Physics.

 

[atyy]

The Laws of Physics by Milton A. Rothman
https://archive.org/details/TheLawsOfPhysics

Old popsci book for lawmakers - talks about some lawmakers who decided to repeal the law of gravity because it was causing so many problems. Unfortunately, they forgot about angular momentum conservation, so everything went whizzing off into space when they repealed the law of gravity.

 

[nrqed]

You know a book which is rarely cited, mentioned or recommended, quite unknown even to the experts, and yet you have discovered that this book is really great? Please share it with us!

My example:
H. Muirhead, The Physics of Elementary Particles
- By style, quality and time of writing very comparable to the famous Bjorken and Drell's Relativistic Quantum Field Theory.

Here is my own partial list (I am not sure if they are all truly undervalued, I just rarely see them mentioned anywhere and yet I learned a lot from them)

All the books by Walter Greiner (that included QFT, QM, the weak interaction, QCD, QED and many more).

"Path Integrals in QM, Statistics, Polymer Physics and Financial Markets" by Kleinert

"Critical properties of Phi^4 theories" also by Kleinert.

"QFT: A Modern Perspective" by Nair

"Algebraic Geometry: A problem solving approach" by Garrity et al

"Geometry, Particles and Fields" by Felsager

"QFT of point particles and strings" by Hatfield

"Introduction to Susy" Muller-Kirsten and Wiedemann

"Introduction to QM: Schrodinger equation and path integral" by Muller-Kirsten

"Mathematics for physics: A guided tour for graduate students" by Stone and Goldbart

"Conceptual foundations of modern particle physics: by Marshak

"Gravitation" foundations and frontiers" by Padmanabhan

"Théories de la relativité" par Uzan et DeRuelle

"E&M for mathematicians" by Garrity

"Basic concepts of string theory" by Blumenhagen et al

"Graphs on surfaces and their applications" by Lando and Zvonkin

"The quantum mechanics Solver: How to apply QM to Modern Physics" by Basdevant and Dalibard

"Enumerative geometry and string theory" by Katz

"Supersymmetry in particle physics: an elementary introduction" by Aitchison

"Gravity and strings" By Ortin

"Glimpses of soliton theory" by Kasman

Ok, I will stop now :-) (and before you ask, yes I do own all of them...plus about another 400 math and physics books)

 

[parshyaa]

General chemistry by linus pauling, is it popular, i liked his style and book with lot of knowledge.

 

[jedishrfu]

I like Nearings Dover book on Mathematical Physics and its freely available on his website:

http://www.physics.miami.edu/~nearing/mathmethods/

His presentation is pretty good and it can be carried on your smart phone or tablet.

 

[snatchingthepi]

A favourite oldie of mine is Fermi's "Thermodynamics". Straight from one of the masters.

 

[nrqed]

I had forgotten those three that I like very much too:"Supersymmetry in particle physics: an elementary introduction" by Aitchison

"Gravity and strings" By Ortin

"Glimpses of soliton theory" by Kasman

 

[MrRobotoToo]

E.B. Manoukian's https://www.amazon.com/dp/1402041896/?tag=pfamazon01-20 is little heard of, but a truly wonderful book. It is perhaps the most comprehensive tome ever written on quantum mechanics; essentially a modern version of Albert Messiah's famous book.

 

[Demystifier]

E.B. Manoukian's https://www.amazon.com/dp/1402041896/?tag=pfamazon01-20 is little heard of, but a truly wonderful book. It is perhaps the most comprehensive tome ever written on quantum mechanics; essentially a modern version of Albert Messiah's famous book.

The book really seems great and undervalued. But Cohen-Tannoudji et al is still bigger (though not undervalued)
https://www.amazon.com/dp/0471569526/?tag=pfamazon01-20

 

[atyy]

E.B. Manoukian's https://www.amazon.com/dp/1402041896/?tag=pfamazon01-20 is little heard of, but a truly wonderful book. It is perhaps the most comprehensive tome ever written on quantum mechanics; essentially a modern version of Albert Messiah's famous book.

Interesting, looks like he's got two volumes of QFT also, the second covering quantum gravity, supersymmetry and string theory!

 

[MrRobotoToo]

The book really seems great and undervalued. But Cohen-Tannoudji et al is still bigger (though not undervalued)
https://www.amazon.com/dp/0471569526/?tag=pfamazon01-20

Completely forgot about that one. I have to admit, Cohen-Tannoudji takes the title of most comprehensive tome, with 1500 pages compared to Manoukian's relatively paltry 986. One thing in Manoukian's favor is that he covers some modern topics that are conspicuously absent in Cohen-Tannoudji, such as Bell's theorem, decoherence, and path integrals.

Interesting, looks like he's got two volumes of QFT also, the second covering quantum gravity, supersymmetry and string theory!

Thanks for the heads up--I had never noticed them before.

 

[nrqed]

The book really seems great and undervalued. But Cohen-Tannoudji et al is still bigger (though not undervalued)
https://www.amazon.com/dp/0471569526/?tag=pfamazon01-20

I just got the two volumes by Manioukan, I am looking forward to reading them.

I would also not call Cohen-Tannoudji undervalued, it was even the textbook used in my undergrad QM one year class. Maybe it is less known in English speaking universities though.

 

[George Jones]

"E&M for mathematicians" by Garrity

"Basic concepts of string theory" by Blumenhagen et al

I ordered these books yesterday from amazon.com and was charged $29.08 and $28.83 respectively. Today, the prices are $116.95 and $115.70. (All prices in Canadian dollars; amounts would be less in US dollars.)

 

[atyy]

I would also not call Cohen-Tannoudji undervalued, it was even the textbook used in my undergrad QM one year class. Maybe it is less known in English speaking universities though.

Probably not, Cohen-Tannoudji was the text for second semester undergraduate qm when I took it at MIT (long ... ago).

 

[Demystifier]

Cohen-Tannoudji was the text for second semester undergraduate qm when I took it at MIT

Wait a minute, I thought you are a biologist? Admit, do you or do you not have a diploma in physics?

 

[atyy]

Wait a minute, I thought you are a biologist? Admit, do you or do you not have a diploma in physics?

I have undergrad degrees in biology and physics. The American system allows two majors, so I did physics also for fun.

 

[Demystifier]

I have undergrad degrees in biology and physics. The American system allows two majors, so I did physics also for fun.

I knew it!
It was just not possible that a pure biologist has a such a damn good knowledge and understanding of physics.

 

[Demystifier]

One thing in Manoukian's favor is that he covers some modern topics that are conspicuously absent in Cohen-Tannoudji, such as Bell's theorem, decoherence, ...

One of the coauthors of Cohen-Tannoudji et al later remedied this deficiency in another great and undervalued book
https://www.amazon.com/dp/110702501X/?tag=pfamazon01-20

 

[atyy]

I knew it!
It was just not possible that a pure biologist has a such a damn good knowledge and understanding of physics.

But you did know I had done physics coursework, right? I think I've mentioned having had statistical mechanics and quantum before.

 

[Demystifier]

But you did know I had done physics coursework, right? I think I've mentioned having had statistical mechanics and quantum before.

No, I missed that.

 

[George Jones]

"Quantum Concepts in Physics: An Alternative Approach to the Understanding of Quantum Mechanics" by Malcolm Longair (2013)
This book, intended to be a compliment to (but not substitute for) standard courses and texts on quantum mechanics, presents quantum mechanics from a historical perspective at about the level of a senior undergraduate. At 400 pages, it is much more digestible than the multi-volume comprehensive work of Mehra and Rechenberg. I have thoroughly enjoyed the parts that I have read.

"Differential Geometry and Lie Groups for Physicists" by Marian Fecko (2006)
Fecko has lots of examples given as short exercises, which might not be a likable style for everyone, but I certainly have learned stuff from it.

"Lectures on Quantum Theory: Mathematical and Structural Foundations" by Chris Isham (1995)
Twenty years ago, I slowly went through this little book, line-by-line. This is one of the very few books for which I have done this. I think that this book, which is not an axiomatic presentation of quantum mechanics, should be read by more physics grad students.

"Quantum Field Theory: A Tourist Guide for Mathematicians" by Gerald Folland (2008)
Although Folland doesn't cover as much as physics texts such as Schwartz or Peskin and Schroeder, Folland does cover a lot more than most rigourous math books on quantum field theory. Folland uses mathematical rigour where possible, and where physicists' quantum field theory calculations have yet to be made mathematically rigourous, Folland states the mathematical difficulties, and then formally pushes through the physicists' calculations. I would be interested in hearing some opinions of physics on this book. I think that book states more clearly some of the standard aspects of quantum field, but I know little about quantum field theory, and I could be wrong.

As a side note, I am trying (sporadically) to learn a little more about quantum field theory, but someone close to me thinks that my efforts are futile.

3. Read a little about quantum field theory, which I didn't learn as a student. My wife, who has an M.Sc. in physics, is a great source of encouragement: "You're to old to learn quantum field theory!"

 

[dextercioby]

@George Jones You do know that Folland's book in 1st (original, 2008) printing had a 5 page errata and the subsequent printings also had errors, right?

 

[MathematicalPhysicist]

"Quantum Concepts in Physics: An Alternative Approach to the Understanding of Quantum Mechanics" by Malcolm Longair (2013)
This book, intended to be a compliment to (but not substitute for) standard courses and texts on quantum mechanics, presents quantum mechanics from a historical perspective at about the level of a senior undergraduate. At 400 pages, it is much more digestible than the multi-volume comprehensive work of Mehra and Rechenberg. I have thoroughly enjoyed the parts that I have read.

"Differential Geometry and Lie Groups for Physicists" by Marian Fecko (2006)
Fecko has lots of examples given as short exercises, which might not be a likable style for everyone, but I certainly have learned stuff from it.

"Lectures on Quantum Theory: Mathematical and Structural Foundations" by Chris Isham (1995)
Twenty years ago, I slowly went through this little book, line-by-line. This is one of the very few books for which I have done this. I think that this book, which is not an axiomatic presentation of quantum mechanics, should be read by more physics grad students.

"Quantum Field Theory: A Tourist Guide for Mathematicians" by Gerald Folland (2008)
Although Folland doesn't cover as much as physics texts such as Schwartz or Peskin and Schroeder, Folland does cover a lot more than most rigourous math books on quantum field theory. Folland uses mathematical rigour where possible, and where physicists' quantum field theory calculations have yet to be made mathematically rigourous, Folland states the mathematical difficulties, and then formally pushes through the physicists' calculations. I would be interested in hearing some opinions of physics on this book. I think that book states more clearly some of the standard aspects of quantum field, but I know little about quantum field theory, and I could be wrong.

As a side note, I am trying (sporadically) to learn a little more about quantum field theory, but someone close to me thinks that my efforts are futile.

Don't think too much of your wife's remark.

As Bohr is creditted of saying:" Nobody understands Quantum Physics".

 

[diogenesNY]

I 'liked' parshyaa's citation of Linus Pauling's _General Chemistry_, which I am reading as we speak... or so I thought. Actually, I am reading Pauling's _College Chemistry. That is a slightly less intensive book for non-majors, whereas _General Chemistry_ was aimed more at undergrad majors.

Anyway, I have no doubt that 'General' is at least as wonderful as 'College'.

_College Chemistry_ is well written, readable, follows a logical and comprehensible sequence and is exceptionally clear. From what I have read elsewhere, the actual chemistry is perfectly functional and accurate except for a specific bit about (I think) nuclear structure... I am not that far yet.

I really wish I had this book back in high school when I was being swamped with a completely incomprehensible high school textbook.

An electronic copy of _College Chemistry_ can be found here:

https://archive.org/details/CollegeChemistry

I have a really nice hardcover copy that I paid 5 or 6 bucks for from either betterworldbooks.com or abebooks.com... I don't recall which. Inexpensively available, and notably, both books are really nice books as books. Really good bindings, cover that will last 200 years, great paper... typeface, etc. Not that that is how we necessarily value such a book, but the sheer quality and sense that it is designed to last and be used is a nice contrast to many contemporary textbooks. (I will refrain from any further textbook rant).

From stem to stern, there is a real pride of quality about both books. It is a nice touch, and perhaps in some small way speaks to pride of authorship, and it seems to be a book that you are meant to keep...

Type "Linus Pauling College Chemistry" into your favorite search engine and you will find a lot of interesting and highly complementary commentary on the book.

It looks like an electronic copy of General Chemistry used to be available on archive.org, but now it is under some sort of lending library checkout system... go figure.

Anyway... I think _College Chemistry_ is strictly top shelf, and I assume that _General Chemistry_ is as well.

diogenesNY

 

[bolbteppa]

Goursat, Course of Mathematical Analysis, 5 volumes.

3 of them are here.

This is the set of books that Bourbaki wanted to rewrite in modern terms, "According to Chevalley the project was extremely naive. The idea was to simply write another textbook to replace Goursat’s", and we know what that turned into, so that tells you all you need to know about these books, and you could treat this as like Volume 0, the intro to Goursat on it's level

 

[Demystifier]

Goursat, Course of Mathematical Analysis, 5 volumes.
3 of them are here.

In addition to those 3, I have found only one book more:
https://www.amazon.com/dp/0486446522/?tag=pfamazon01-20
What is the last volume?

 

[bolbteppa]

They merged them into one in that version!

 

[MathematicalPhysicist]

Goursat, Course of Mathematical Analysis, 5 volumes.

3 of them are here.

This is the set of books that Bourbaki wanted to rewrite in modern terms, "According to Chevalley the project was extremely naive. The idea was to simply write another textbook to replace Goursat’s", and we know what that turned into, so that tells you all you need to know about these books, and you could treat this as like Volume 0, the intro to Goursat on it's level

Thanks for pointing this series to me.

It seems also Barry Simon's comprehensive series is more modern counterpart to Goursat's 5 volume series.

So many books to own so little money... :-(