Lie Groups and Lie Algebras For Physicists

This book systematically introduces the basic concepts of Lie groups and Lie algebras, their representations and reductions, and thoroughly discusses the connections between abstract mathematical concepts/principles and physical concepts/principles. It explores the applications of Lie groups and Lie algebras in the study of particle physics and fundamental interactions, as well as algebraic methods for many-particle systems and their applications (in nuclei, molecules, superconductivity, etc.), thus building a bridge between actual scientific research and the study of fundamental theories. The book consists of eight chapters. Chapter 1 introduces the basic concepts of Lie groups and Lie algebras. Chapter 2 covers semisimple Lie algebras and their root systems. Chapter 3 presents realizations of classical Lie algebras. Chapter 4 discusses representations of classical Lie algebras and Lie groups. Chapter 5 addresses the reduction of representations of classical Lie algebras and Lie groups. Chapter 6 examines spacetime symmetry and its applications in the study of properties of particles and fields. Chapter 7 discusses the applications of classical Lie algebras in the study of hadron structure and the laws of fundamental interactions. Chapter 8 covers the applications of classical Lie algebras in the study of properties of many-particle systems. This book is suitable as a textbook or reference book for a course on "Lie Groups and Lie Algebras" or "Group Theory II" for physics majors, and may also serve as a reference for young researchers.