aalaniz

Note previous files BS1 - BS4 condensed to just Lie.PDF. New stuff p. 251-293 quantum physics of spin, orbital and total angular momentum, tensor products, direct sums, ladder operators, Young's tableaux, root and weight diagrams leading to Dynkin diagrams.

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The well known physicist John Baez has posted a copy of this work on his site and is pointing his large readership to join Physics Forums as a valuable site. Garrett Lisi has also sampled...

Shrinking the madness. Go to the Wikipedia article on the Special Linear Group. This article will lead you to many other articles, e.g., Polar decomposition, SL2(R), Mobius transformation (fractional linear transformation (review Complex Variables), Modular Group (to Braid group), the Exponential Mapping, Casimir Invariants, and so on. Most of these links are circular exactly in the sense of mathematics. What some derive as theorems of a set of axioms, others take as their set of axioms, and...

http://www.ima.umn.edu/~miller/lieth...functions.html

Professor Miller's book is very readable, presuming some background readings such as the books by R. Gilmore and the book by H F Jones 2nd ed. Chapter 5 of Nakara adds another dimension to the Lie derivative.

It's hard to find literature connecting Lie's work to the differential equations and special functions of mathematical physics. Miller (1968) is such a source, and good.

Cheers,
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Depending on your background, the introductorry book on Loop Quantum Gravity by Gambini and Pullin is a pretty good and succint. As a non-specialist who likes keeping current with today's foundation physics, I found my readings from the following sources to be pretty essential:

For Gambini's and Pullin's chapters 2 and 3:

1) "A Short Course in General Relativity" by J. Foster and J. D. Nightingale.

For Gambini's and Pullin's chapters 4-6:...

My family and I had the pleasure of spending this Thanksgiving with close friends at Los Alamos. I had a chance to discuss math foundations and genetics with Elena, a mathemetician into genetics, and quantum mechanics with Vincenzo, a particles and fields theoretician.

Vincezno and I read and discussed the paper, "The quantum state cannot be interpreted statistically" by Matthew F. Pusey, Jonathan Barrett, and Terry Rudolph ( lanl.arXiv.org > quant-ph > arXiv:1111.3328...