Linear Algebra and Group Theory for Physicists

Contents: Preface. 1. Elements of Group Theory. 2. Some Related Algebraic Structures. 3. Linear Vector Space. 4. Elements of Representation Theory. 5. Representations of Finite Groups. 6. Representations of Linear Associative Algebras. 7. Representations of the Symmetric Group. 8. The Rotation Group and its Representations. 9. The Crystallographic Point Groups. 10. The Lorentz Group and its Representations. 11. Introduction to the Classification of Lie Groups ­ Dynkin Diagram. Index.

"Professor Srinivasa Rao's text on Linear Algebra and Group Theory is directed to undergraduate and graduate students who wish to acquire a solid theoretical foundation in these mathematical topics which find extensive use in physics. Based on courses delivered during Professor Srinivasa Rao's long career at the University of Mysore, this book is remarkable for its clear exposition of the subject.Advanced students will find a range of topics such as the representation theory of linear associative algebras, a complete analysis of Dirac and Kemmer algebras, representations of the symmetric group via Young tableaux, a systematic derivation of the crystallographic point groups, a comprehensive and unified discussion of the rotation and Lorentz groups and their representations, and an introduction to Dynkin diagrams in the classification of Lie groups. In addition, the first few chapters on elementary group theory and vector spaces also provide useful instructional material even at an introductory level.

This book provides a solid theoretical foundation as opposed to others devoted primarily to applications. A complete resolution of two-sided and minimal ideals of the Dirac and Kemmer algebras; a unified approach to the Rotation and Lorentz groups; classification of compact simple Lie algebras and Dynkin diagrams are among the topics covered."