Ma Z.-Qi, Gu X.-Y. Problems and solutions in group theory for physicists

World Scientific Publishing Company, 2004. — 476 p. — ISBN 98 1-238-833-8.This book is aimed at graduate students in physics who are studying group theory and its application to physics. It contains a short explanation of the fundamental knowledge and method, and the fundamental exercises for the method, as well as some important conclusions in group theory.
Group theory is a powerful tool for studying the symmetry of a physical
system, especially the symmetry of a quantum system. Since the exact
solution of the dynamic equation in the quantum theory is generally difficult
to obtain, one has to find other methods to analyze the property of the
system. Group theory provides an effective method by analyzing symmetry
of the system to obtain some precise information of the system verifiable
with observations. Now, Group Theory is a required course for graduate
students major in physics and theoretical chemistry.Review on linear algebras
Group and its subsets
Theory of representations
Three-dimensional rotation group
Symmetry of crystals
Permutation groups
Lie groups and lie algebras
Unitary groups
Real orthogonal groups
The symplectic groups