This book is intended as an introduction to group representation theory, emphasizing its natural role as the mathematical framework to describe symmetry properties of classical and quantum mechanical systems. It is written at the graduate and advanced undergraduate level, and is suitable either as a textbook or for self-study.
Because of the fundamental importance of symmetry considerations in all branches of physics, familiarity with basic group concepts and techniques is invaluable in the education of a modern-day physicist irrespective of his special field. This book emphasizes general features and methods which explicitly demonstrate the power of the group-theoretical approach in exposing the systematics of physical systems with associated symmetry. It seeks to provide a deeper and more unified understanding of results previously encountered by students in classical and quantum physics, as well as to introduce more powerful group-theoretical methods not seen in traditional textbooks.
Particular attention is given to pedagogy. Simple illustrative examples are given to motivate each important general topic before the formal theory is presented. In developing the theory. clarity in presenting the main ideas and the consequences is given priority over comprehensiveness and strict rigor. Non-essential details arc avoided as much as possible in the main text. To preserve the integrity of the mathematics however, enough technical information is included in the appendices to make the book almost self-contained. Many examples and applications are given in each chapter after the presentation of the theory.