Matt Haley's Physics Site

Undergrad Books

Snieder. A Guided Tour of Mathematical Methods.
Certainly not the most advanced of math books, but this one does a nice job of explaining Fourier integrals and transforms, Green functions, delta functions, and the connection of those things with linear algebra. It has good physical examples too. Highly recommended for undergrads or beginning grads trying to get a more intuitive grasp on certain math subjects. I didn't read the beginning, but it looks like a slightly more advanced "Div, Grad, Curl, and all That," another informal classic.

Shankar. Principles of Quantum Mechanics.
Awesome book in every regard. The introduction is a perfect overview of the math needed to really get going with QM, and the detailed example of the coupled mass-spring system used to demonstrate switching bases is excellent. Despite this being a beginner's book, it is surprisingly detailed too, and I often find myself referring back to it for random things.

Grad Books

Lahiri, Pal. A First Book of Quantum Field Theory.
This book is reminiscent of Mandl Shaw, another popular "easy" QFT book, but this one's better overall. Mandl Shaw starts out by throwing the Fourier decomposition of the field at you straight away instead of easing you into the subject, following the seeming physics authoring trend of containing an introduction that's only comprehensible once you've finished the book. (Do physics authors know what conclusions are for?) The Lahiri Pal introduction is very readable though, and technicality ramps up in a reasonable way. Also, the writing style of this book is very concise and entertaining. Some chapters read almost like mysteries, starting with puzzles that await solving--much better that the usual approach of meandering without any strategy the reader is aware of. I really like certain sections of Mandl Shaw, such as the explanation of QED Feynman diagrams in Ch. 7, but all in all Lahiri Pal is a much smoother intro to QFT, not because it's easier or dumbed down, but because it's just plain better. My favorite part is the awesome calculation of the anomalous magnetic moment of the electron in 11.3. Hopefully this excellent book's popularity will increase!

Aitchison, Hey. Gauge Theories in Particle Physics.
I've spent many an evening with these books (vol 1 and 2) learning the consequences of symmetries. The Yang-Mills fields resulting from SU(2) symmetry and gluon fields from SU(3) are nicely introduced here. Again, a feature of this book that makes it great is the effort taken to explain things while consciously looking back and looking forward in the material to give everything an integrated feel. As an example, the subsection about differential geometry during the discussion of covariant derivatives was very welcomed. The new 3rd edition is quite spiffy looking too.

Other Favorite Books

Vonnegut, Kurt. Sirens of Titan.
This isn't exactly a science book, but I think it admirably conveys a fundamental philosophical outlook of science--and in a manner which happens to be outrageously entertaining. This is a VERY quirky story by the master of quirky stories, and somehow its quirkyness fits in exactly with the theme of our ultimate purpose here on earth (and on mars). It's hard to find great writers who also have a scientific outlook on the universe, but Kurty Kurt has this for sure. In fact, he studied engineering at one point in his life! (Those who have read a few Vonnegut books will recall the character Kilgore Trout, a prolific science fiction writer who knows nothing about science.) When I had the pleasure of speaking with him once, he said regarding the prejudice of the literary community against science, "They think you can't write a good book if know how your refrigerator works."

Favorite Equations

The Gell-Mann--Nishijima Relation:

The Divergence Theorem:

Loosely speaking, this equation says that however much of the field F is created within a volume (left hand side), the same amount must be emanating through the surface of that volume (right hand side). While not exaclty an advanced math equation, I've always liked it for its clear intuitive statment and its immediate application in Gauss's Law. If you're new to this important equation, a good place to read about it is in Schey's Div, Grad, Curl and all That.

Politzer, Gross, and Wilczek law:

This formula is the lynchpin of QCD, the theory of the strong nuclear force. The parameter αs is the strong coupling constant that determines the strength of the interaction. You can easily see that as the momentum q2 increases (or equivalently, as the distance between interacting quarks decreases), the strong force subsides, since the coefficient on the ln term is positive and ln just keeps growing. This is the all-important property only present in the strong force called asymptotic freedom, which is related to quark confinement. In QED (quantum electrodynamics), the situation is similar with the big exceptionof there being a negative coefficient on the ln term, implying that the electric force is stronger at very close range and weaker farther away. The QED property is thus called "screening", while the curious QCD property is called "anti-screening".

More Coming!

If you've made it all the way down here, you're clearly privileged to hear this bad joke I came up with.
Q: How did the necrophiliac lose his innocence?
A: He obtained charnel knowledge.