Groups and Symmetries: From Finite Groups to Lie Groups

Groups and Symmetries: From Finite Groups to Lie Groups is a comprehensive introduction to the theory of group representations and their applications in quantum mechanics. It covers finite groups, compact groups, linear Lie groups, and their Lie algebras, with an additional chapter on Clifford algebras, spin groups, and the theory of spinors. The text is accessible to advanced undergraduates in mathematics and physics and beginning graduate students, and includes references for further study. Each chapter ends with exercises and problems with complete solutions.

Format: Paperback / softback
Length: 251 pages
Publication date: 17 July 2022
Publisher: Springer Nature Switzerland AG

Groups and Symmetries: From Finite Groups to Lie Groups is a comprehensive introduction to the theory of group representations and their applications in quantum mechanics. Written with accessibility in mind for advanced undergraduates in mathematics and physics, as well as beginning graduate students, the text covers the theory of representations of finite groups, compact groups, linear Lie groups, and their Lie algebras, all in a single volume. Prerequisites include calculus and linear algebra.

In this updated edition, an additional chapter has been included, delving into Clifford algebras, spin groups, and the theory of spinors. Furthermore, new sections titled "Topics in history" have been added, providing notes on the historical development of the material covered in each chapter. These historical notes collectively form an account of the evolution of group theory from its inception in the 18th century to the mid-20th century.

Each chapter concludes with a collection of exercises, ranging in difficulty, some introducing new definitions and results. The text concludes with a comprehensive collection of problems with complete solutions, making it an ideal resource for both course work and independent study.

Key topics covered in this text include:

A concise review of the fundamental concepts of group theory, with examples

Representation theory of finite groups: Character theory

Representations of compact groups using the Haar measure

Lie algebras and linear Lie groups

In-depth study of SO(3) and SU(2), and their representations

Detailed exploration of spherical harmonics

Representations of SU(3), roots, and weights, with quark theory as a consequence of the mathematical properties of this symmetry group

Spin groups and spinors

By presenting the theory of group representations in a clear and concise manner, Groups and Symmetries: From Finite Groups to Lie Groups serves as an invaluable resource for students seeking to deepen their understanding of this fundamental mathematical discipline. Its applications in quantum mechanics make it particularly relevant to those interested in pursuing careers in physics and mathematics.

Weight: 456g
Dimension: 154 x 234 x 16 (mm)
ISBN-13: 9783030943592
Edition number: 2nd ed. 2022