Free Ebook Elements of group theory for physicists, by A. W Joshi
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Elements of group theory for physicists, by A. W Joshi
Free Ebook Elements of group theory for physicists, by A. W Joshi
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- Sales Rank: #6454832 in Books
- Published on: 1977
- Number of items: 1
- Binding: Paperback
- 324 pages
Most helpful customer reviews
2 of 2 people found the following review helpful.
A superior treatment of continuous groups
By Ulfilas
This readable introduction to group theory for physicists strongly resembles Tinkham's book Group Theory and Quantum Mechanics and has a virtually identical choice of topics. Where Joshi differs from Tinkham, however, is in his more detailed treatment of continuous groups. Joshi begins his discussion of continuous groups with a better introduction of topological concepts such as connectedness and compactness that makes use of especially helpful and useful figures. The matrix representations of Lie groups are explained in terms of the their associated generators--a treatment that I find very satisfying and complete. The topology of the SO(3) group is given special attention, using diagrams in such a way that the reader is actually able to understand what is meant in saying that this group is doubly connected. I have scanned and attached a figure from Joshi illustrating this concept.
The Lorenz group is also explained in a very gradual and understandable way, beginning with the observation that it is a pseudo-rotation group that in its two dimensional analogue leaves the quadratic form x**2-y**2 invariant. From there you see that the hyperbolic functions sinh and cosh are the necessary elements in the pseudo-rotation matrices that correspond to Lorentz transformations. Joshi is also extremely generous in his detailing of the various differential generators used to represent rotations and boosts.
It is also worth noting that Joshi treats elastic constants as well as piezoelectricity and dielectric susceptibility, topics that are generally not given any mention in group theory books--but which you find discussed in Nye's book Physical Properties of Crystals: Their Representation by Tensors and Matrices.
6 of 6 people found the following review helpful.
Understand Quantum Mechanics and Solid State Theory
By Arthur
Group theory... Ever heard about it? Want to understand what really happens, from the mathematical standpoint of view, in quantum mechanics, crystallography, symmetries and solid state physics? Ever found some band structure graphic and had no idea of its meaning? Tired of computer simulation without knowing the 'guts' of that first-principles? I found what I needed in terms of group theory in this book. The undergraduate course of chemistry, and perhaps physics as well, just give us hints about solid state. But this book have much to offer for any reader. Starting with abstract group theory from the very basic ending in solid state physics, going through extensive but not exhaustive analysis of quantum mechanics, it is a must read not just for all who deal with theory but also to anyone who really want to understand energy bands, level splitting, and an infinite number of must-know topics in today's thin border between chemistry and physics.
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