What Undervalued Books Have You Discovered?

[Demystifier]

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.

 

[dextercioby]

x₄ = ict, awful. Go home, throw this in the trash bin.

 

[Useful nucleus]

Thermodynamics by Radu Paul Lungu. I did not read all of it, but I was impressed by the very precise and thorough of treatment of thermodynamics under electric and magnetic fields. There are many subtle points in this topic and this text is the only one I found that addressed many of these subtleties in a clean way.

 

[jasonRF]

Waves and Distributions by Jonsson and Yngvason from University of Iceland is a great little book designed to be used for a focused undergrad math methods course (advanced undergrad or beginning grad level in US). The title is perfectly chosen to give you the idea of the book. I really like chapters 4-6, which in 120 pages present a very concise version of distribution theory and Fourier analysis, then uses them consistently to analyze elementary problems in radiation, guided waves, and propagation in dispersive media. It is quite mathematical for a math methods book as it certainly requires undergraduate intro real analysis so freely uses $\sup$, etc., and assumes the associated maturity. A few passages are more abstract than I would prefer (radiation in N-dimensional space, etc) and it is probably not be the best place to learn most of the material for the first time (spherical harmonics, wave guides, Huygen's principle, etc.), but the way everything is threaded together in one place tells a story that is a treat to read. Chapter 6 on dispersive media is particularly good; I wish I had read it prior to taking any plasma physics.

 

[Demystifier]

x₄ = ict, awful. Go home, throw this in the trash bin.

Well, I didn't say it's perfect.

 

[martinbn]

Kostrikin, Manin "Linear Algebra and Geometry", I don't know if it is undervalued, but it seems to me that it isn't very popular. I found it very good.

 

[vanhees71]

The theory series in 6 volumes by Sommerfeld is rarely used nowadays, which is a pity since I think it's still one of the best and clearest assessments of classical theoretical physics, even after about 50-60 years (he's even so "modern" to use the SI units in electromagnetism and optics, which I personally see rarther as an disadvantage, but I'm quite lonely with this opinion either ;-)). Of course, also here the ict convention is used in relativity, but that's the only mishap but quite common at the time of writing.

The same holds for the theory series (also in 6 volumes) by Pauli. It covers all classical physics (except mechanics), QM, and QFT. The latter, however, is completely outdated although it contains a thorough discussion about the various invariant functions like propagators, commutators, etc. in the time-position domain which are not found easily in modern books on the subject.

 

[MathematicalPhysicist]

Well, three years ago I started reading Schwinger's book on Source theory, first volume.

I should come back to it one day and read it more carefully, I might also add a thread in QP subforum with questions on this three volume treatise.

I am not sure how well do people know this book.
Another book on Nuclear Physics from Judah Eisenberg and Walter Greiner's book, I started reading it last year; stopped with it a few months ago.
I need someday find a time to read Cohen Tannoudji's - Zelevinsky's - Judah Eisenberg's;

In Eisenberg's book obviously they assume knowledge of QM especially Clebsch-Gordan coeffcients, there appear there some nifty special functions such as Grinbauer special functions (I am not sure about the name, but I am sure it started with the letter 'G'), and some also interesting recusrion relations.

Cool stuff!
Edit: here is the special function:
https://en.wikipedia.org/wiki/Gegenbauer_polynomials

 

[Amrator]

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.

Why is it a good book?

 

[Demystifier]

Why is it a good book?

Because it is quite similar to Bjorken and Drell. If B&D is good (and many agree that it is), then so is this book.

 

[vanhees71]

Yes, Bjorken&Drell is the classic concerning QFT. Forget volume 1, but volume 2 is still a good source.

 

[MathematicalPhysicist]

Yes, Bjorken&Drell is the classic concerning QFT. Forget volume 1, but volume 2 is still a good source.

Why forget Relativistic QM?

How would people know how did we come to point C from point A without crossing through point B.

What are the merits of forgetting Relativistic QM? I wonder.

 

[vanhees71]

The merit is that you don't need to bother with an inconsistent predecessor theory to modern QFT. It's only interesting in the sense of the history of science. To understand relativistic QT it rather confuses students more than it helps, and QFT is difficult enough. You won't need additional problems that are solved for decades now!

 

[MathematicalPhysicist]

I don't know really.

In my university in the undergraduate QM2 we learned of Relativistic QM (it was in 2010-2011), I assume pedagogically in my university they don't think like you.

Are you sure that modern QFT isn't plagued with inconsistencies as well?:-)

 

[vanhees71]

Well, yes, there are inconsistencies, but much less than in a theory, where you claim to describe strictly one particle, only to resolv it by introducing a state of infinitely many particles whose existence is then handwaved away to then claim that only the holes in this sea of nonobservable particles are observable as antiparticles. Why should I teach my students such a confusing argument instead of starting right away with the many-body description of renormalized perturbative QFT and the Standard Model which is more successful in the description of all visible matter known today?

 

[S.G. Janssens]

Why should I teach my students such a confusing argument instead of starting right away with the many-body description of renormalized perturbative QFT and the Standard Model which is more successful in the description of all visible matter known today?

The only argument I can come up with is: Because it is an (epistemological) illustration of how theory develops.
?

Please do not misunderstand me: For me this argument would probably not be convincing! (In my own field I generally find it very confusing when modern concepts are taught through discussion of their historical origins. Incidentally, one exception is the beautiful book on one-parameter semigroups by Engel & Nagel that develops the modern theory of operator semigroups for linear evolution equation starting from a discussion of the (scalar) exponential.)

 

[MathematicalPhysicist]

So @vanhees71 at your school where you teach, they don't teach relativistic QM?

 

[MathematicalPhysicist]

The only argument I can come up with is: Because it is an (epistemological) illustration of how theory develops.
?

Please do not misunderstand me: For me this argument would probably not be convincing! (In my own field I generally find it very confusing when modern concepts are taught through discussion of their historical origins. Incidentally, one exception is the beautiful book on one-parameter semigroups by Engel & Nagel that develops the modern theory of operator semigroups for linear evolution equation starting from a discussion of the (scalar) exponential.)

Hi @Krylov if I remember correctly you said once that your expertise lies in Control Theory, how well versed are you in this field?
I might have in the future some questions from books in Control Theory so it will be good if I would have a correspondent, in my university there aren't a lot of experts in this field.

 

[Demystifier]

It's only interesting in the sense of the history of science.

There are other merits too.
1) Solution of the Dirac equation (without QFT interpretation) gives the spectrum of the hydrogen atom, more accurately than the non-relativistic Schrodinger equation.
2) The perturbative calculation of scattering amplitudes in string theory is better viewed as a generalization of Bjorken-Drell 1 than of Bjorken-Drell 2.

 

[vanhees71]

So @vanhees71 at your school where you teach, they don't teach relativistic QM?

I once had to give the lecture Quantum Mechanics 2. There I taught right away QFT and not relativistic QM since I find relativistic QM more confusing than relativistic QFT which is the relativistic QT really working (and with great success) despite the quibbles you can have with it since the mathematical foundation for the interacting case is somewhat shaky. However it's the best theory we have, and it's the only form it's used in physics research today. I don't know, why I should teach an outdated intrinsically inconsistent concept. There's no application for it which cannot also be covered with QFT. In this QM 2 lecture I ended with the derivation of the Feyman rules for QED and the evaluation of the most important tree-level scattering processes. The students were very enthusiastic about is in their evaluation. Their only complaint was that they would have liked more relativistic QFT instead of the non-relativistic many-body theory, I had to cover within this lecture first .

I also don't teach Aristotelian physics before I start with Newtonian mechanics or "old quantum mechanics", i.e., Bohr-Sommerfeld quantization or the wrong picture of photons a la Einstein 1905.

 

[MathematicalPhysicist]

So why do people still teach Newtonian mechanics in first year, if it's outdated?

Your argument is a bit shaky, but granted this is a subjective issue.

 

[vanhees71]

Newtonian mechanics is not outdated. It's still a valid approximation. It's pretty obvious that you cannot start to learn physics by jumping right away to General Relativity and (special) relativistic QFT since you need some prerequisites from classical non-relativistic and relativistic physics first to make sense out of QT at all.

What's outdated is "old quantum mechanics" and "relativistic QM" since the former is pretty useless given the modern theory and the latter is inconsistent. Thinking it through (as Dirac did with his wave equation) you come to the conclusion that there is no one-particle interacting relativistic QM. The reason is that in reactions at relativistic energies you are producing and destroying particles easily, and that's why you necessarily have to deal with a formulation, where such creation and annihilation processes are included. Dirac developed his "hole theory" from it, i.e., he introduced his "Dirac sea" and then developed QED with this concept. It turns out that his hole theory is equivalent with modern QED based on QFT, but it's much more confusing than the modern formulation. That's why I think one should teach relativistic QT right away as relativistic QFT.

 

[vanhees71]

There are other merits too.
1) Solution of the Dirac equation (without QFT interpretation) gives the spectrum of the hydrogen atom, more accurately than the non-relativistic Schrodinger equation.
2) The perturbative calculation of scattering amplitudes in string theory is better viewed as a generalization of Bjorken-Drell 1 than of Bjorken-Drell 2.

1) can be done entirely in the QFT framework (see Weinberg QT of fields I). There isn't much difference to the "oldfashioned" treatment, and it's conceptually very easy to implement quantum corrections (i.e., the Lamb shift).

I can't comment on 2) since I'm not famliar with string theory.

 

[Demystifier]

@vanhees71, can you recommend some undervalued book? (Weinberg of course is not undervalued.)

 

[vanhees71]

I already did above. I think the Theory series by Sommerfeld and Pauli are undervalued. Although they are quite old, they still are pretty up to date (in the Pauli case with the exception of the QFT volume).

 

[atyy]

But if you don't teach for at least 5 seconds relativistic QM, how do you explain why such a confusing term as "second quantization" exists, which no longer means what it used to mean?

Also, it's fun to know Dirac's brilliant square root argument.

So I think one can spend at least 5 seconds on relativistic QM.

 

[ShayanJ]

Quantum Field Theory of Point Particles and Strings, Brian Hatfield
Special Relativity in General Frames, Eric Gourgoulhon
Introduction to Quantum Effects in Gravity, Viacheslaw Mukhanov & Sergei Winitzki

I think its good to familiarize students with relativistic quantum mechanics so that they understand why it was necessary to consider fields. Of course I don't mean teaching it in detail, just tell them the story! It wouldn't take more than an hour.

 

[vanhees71]

Sure, some history is never wrong, but I hate the long arguments, insisting on a single-particle picture only to be finally forced to use a many-body picture.

@atyy: What's the square-root argument? Do you mean the introduction of the Dirac matrices in the original paper? That's indeed brilliant as everything written by Dirac, but his textbook doesn't fit here, because it's not undervalued at all (and rightfully so!).

 

[Logical Dog]

A brilliant series used to teach mathematics undergrad, ELIAS ZAKON..FREE

http://www.trillia.com/products.html

 

[atyy]

@atyy: What's the square-root argument? Do you mean the introduction of the Dirac matrices in the original paper? That's indeed brilliant as everything written by Dirac, but his textbook doesn't fit here, because it's not undervalued at all (and rightfully so!).

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".

 

[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)