Group Theory: Application to the Physics of Condensed Matter

This is a modern group theory book compared to the classic group theory book written by, e.g., Tinkham, in the sense that many topics on condensed matter/solid state physics with details and examples are included in the book, which is rarely found in other group theory books. However, not all the chapters are presented in the most comprehensible way, and there are places (especially in the later part of the book on space groups) where things aren't always made very clear. I recommend to read A. Zee's "group theory in a nutshell for physicists" (very friendly and clear to beginners) and perhaps even read the book by "Tinkham", before starting to work on this book,

Notation in the book is bad, makes it hard to read.For example, in the same equation can be used R_n - for translations, and R_alpha for rotations. Confusing.

This book appears not to intend as an introduction for either the group theory or the quantum theory, but for those who already learned basics of those theories and would like to advance further to the application for the solid state physics.It starts with a rough review of the basics (such as the Great Orthogonality Theorem) and speeds up to the applications to the quantum mechanics and solid state physics.It covers a good amount of topics including IR and Raman vibrations and quite well written.The only flaws I noticed are several trivial typos and lacks of the definition of jargon (they sometimes use a little bit unusual expressions such as the Wonderful Orthogonality Theorem instead of the Great Orthogonality Theorem or Schur's Orthogonality Relation without mentioning the difference from the common names) and symbols (as the tech books usually do).I totally recommend this book for the people with basics and would like to learn how those theories are connected and applied to the solid state physics.

「応用群論」と「物質の対称性と群論」の後に読むことで、これらの教科書では理解しにくかった部分をクリアにすることができる。この三冊を読み込めば、物性物理に必要な群論はおよそ習得できると思う。

I like this book very much. It gives a detailed description of group theory and its applications to condensed matter physics. It has many nice figures and a deep explanation of symmetries and their manifestation in group theory.