book reviews
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Reviewed by T. Nelson
Weinberg's Lectures on Astrophysics consists of four big chapters: stars, binary stars, the interstellar medium, and galaxies. The presentation is mathematical, but there's no quantum mechanics and relativity is mainly used in the chapter on binary stars.
Much of the material is standard astrophysics, but with a strong emphasis on calculating. Even so, it's not as abstract as his other mathematical physics books. It's oriented toward calculating phenomena that are potentially observable. For example, the chapter on binaries focuses mainly on gravitational waves and has a great discussion of LIGO. All of it is written in Weinberg's uniquely clear and understandable style.
I had expected more of a particle physics approach, and there's some of that, but mostly Weinberg describes how to calculate diameters of stars, how they collapse, and energy balance within stars, using equations like the collisionless Boltzmann equation, radiative transport, and classical physics. He discusses equations useful for analysis of neutron stars, close binaries, and galactic spiral arms. The chapter on the interstellar medium also discusses soft Bremsstrahlung and accretion spheres.
apr 05, 2020
Reviewed by T. Nelson
This was one of at least four books intended to teach math to physicists. Acquiring the knowledge to get from graduate-level physics to the frontiers of M theory is, as the authors say, a “formidable challenge.” This one is a first step, and it's a doozy.
The main part of the book is Chapter 3, which talks about Lie groups, SO(2), SO(3), SU(2), SU(3), and Lorentz groups. SU(3) is pretty straightforward if you have SU(2), and the author covers them all reasonably well, pausing here and there to explain what the results actually mean in terms of the physical world. But I found many points where I had to page back and re-read an earlier section before I could follow his math. This will be a problem for readers unable to spend the time re-reading parts of this challenging book. I'd recommend at least reading Physics from Symmetry first to get a running start on all the Lagrangians and the math basis for these Lie groups. It also wouldn't hurt to be conversant with special relativity to gain familiarity with some topics. And you'll need at least undergraduate level understanding of quantum mechanics to understand the results.
The next part, Chapter 4, is also a bit of a challenge. Some parts are easy to follow and some require time and effort. Robinson writes [p.263]:
When first learning it, students often feel that the Standard Model is a tool to take a set of beautifully elegant mathematical tricks and turn them into something hideous.
Non-physicists would call this an understatement. But you'll find that more advanced books take your knowledge of this stuff for granted.
Then there's the mathematical skullduggery. It seems like a fundamental principle of quantum field theory that if an infinity turns up in your equation, you throw it away. It's as if you were in a fancy restaurant and your waiter hands you the bill:
WAITER: | Your bill, sir, Infinity dollars and seventy-five cents. |
YOU: | Here you are, my good man. One dollar, and keep the change. |
WAITER: | Thank you so very much, sir. |
The advantage of this book is that it gives a reason for each mathematical step. The author recognizes that most of us don't really care about the math; what we really want is the prize at the end, which is an understanding of nature. That approach permeates the book, making it one of the most readable—but very challenging—mathematical books I've ever seen.
The author says later books in the series will cover gauge theory. I'd buy those in a heartbeat, but so far they haven't been forthcoming. It's starting to look like Ewens's Mathematical Population Genetics vol I, which turned out to be the only one in the series.
apr 24, 2020
Reviewed by T. Nelson
If you enjoy reading books where every equation is pulled out of a hat, making you say “How the heck did he get that???” over and over, you'll love this book!
Of course the purpose of this semi-popular book isn't to explain the formulas. The goal is to help the reader get used to the math behind quantum field theory so they can say things like “Oh yes, that's a Pauli matrix!“ when they see a σ. It covers some of the same topics as Physics from Symmetry (reviewed below) including group and gauge theory but without quaternions and with fewer Lagrangians but more Feynman diagrams.
The goal isn't to teach you QFT—although you'll learn some—but to explain the rationale for the equations that are used, grounding them as much as possible in how they relate to actual particles. You will learn why one approach was used and not some other. Physics from Symmetry was clearer on group theory; this one is clearer on QED, and it has a nice overview of path integrals and a list of Feynman rules.
But of course you don't really understand a formula until you know where it came from. Readers who need a verbal explanation of what a F_{μν}F^{μν} actually does in physical terms will still be mystified. What we really need is something that gives us practice following the derivations, as Tensors, Relativity, and Cosmology by Dalarsson & Dalarsson does for tensors.
The chapter titles of Aperitif, Hors d'Oeuvres, Chef's Secrets, Entrées, and Trou Normand are just gimmicks to make it friendlier; for dessert you get supersymmetry, general relativity, and quantum gravity at about the same semi-popular level. Enough to whet your appetite without risking quantum gastroenteritis.
may 19 2020
Reviewed by T. Nelson
Jakob Schwichtenberg is the author of No-Nonsense Quantum Mechanics: A Student-Friendly Introduction, a much-not-hated book that's a great way for beginners to learn QM without the excessive verbosity, bad jokes, and skipped steps in some other books. In Physics from Symmetry, Schwichtenberg used the same approach to teach the mathematical stuff you need to know before going on to gauge theory and other more advanced topics.
But holy cowing cow, the typos. The errata list on the internet has pages and pages of them, and it's still incomplete. I never before saw an errata list with errors in it. Do not buy this book. Instead get the second edition, which has most of them corrected.
After introducing quaternions, spinors, Lie group theory, and Lagrangians, Schwichtenberg discusses U(1) and SU(2) symmetry. These are useful for understanding electromagnetism and the weak force. The main goal is to keep the equations Lorentz-invariant, and the Higgs mechanism is needed to get a locally SU(2) invariant Lagrangian that includes mass terms. A new factor, which is not a fudge factor at all, hardly, was needed to account for parity violation after experimentalists discovered that only left-chiral particles interact via the weak force. Finally there is a brief discussion of SU(3) and quark color charge.
Although the author does indeed try not to skip steps, the reader needs to know some things to avoid getting bogged down. For instance, on page 63 in the chapter on Lie group theory you'd be totally stumped if you didn't know about the Taylor series expansion of cosh(x). And in Chapter 7 (Interaction Theory), there are entire pages deriving Lagrangians, with their partial differential equations, which get cumbersome.
Once you get through Lie algebra, the rest of the book is more about things that are real, i.e. parts of QM, QFT, relativistic mechanics, and electrodynamics. One of the most important principles in physics is Noether's theorem, which says for every differentiable symmetry there is a corresponding conservation law.
There are a few appendices in the back on basic math. Schwichtenberg has a whole series of “No Nonsense” books.
apr 09 2020