Group Theory for Physicists

This textbook explains the fundamental concepts and techniques of group theory by making use of language familiar to physicists. Calculation methods in the context of physics are emphasized. New materials drawn from the teaching and research experience of the author are included. The generalized Gel'fand's method is presented to calculate the matrices of irreducible representations of the simple Lie algebra and its Clebsch–Gordan coefficients. This book is for graduate students and young researchers in physics, especially theoretical physics. It is also for graduate students in theoretical chemistry.
Contents: PrefaceReview on Linear AlgebrasGroup and Its SubsetsTheory of RepresentationsPermutation GroupsThree-Dimensional Rotation GroupSymmetry of CrystalsLie Groups and Lie AlgebrasGel'fand's Method and Its GeneralizationUnitary GroupsReal Orthogonal GroupsLorentz GroupsSymplectic Groups
Readership: Graduate students and researchers who are willing to explore the mathematical beauty of symmetry. Group Theory;Theory of Representations;Lie Groups;Lie Algebras;Three-Dimensional Rotation Group;Symmetry of Crystals;Young Operators;Unitary Groups;Real Orthogonal Groups;Symplectic Groups0Key Features:Both the theoretical framework of group theory and the calculation technique in physics are emphasized and explained by language familiar to physicistsThe generalized Gel'fand's method is presented and explained in detail by examples for the simple Lie algebrasThe irreducible bases of the symmetry group of a regular icosahedron are calculated explicitly through its isomorphic relation with the alternative subgroup of the permutation group of five objectsOnly based on the translation symmetry of crystals, the crystals are classified completely, and the irreducible representations of the space groups are calculatedAn exercise book "Problems and Solutions in Group Theory for Physicists" (published by World Scientific in 2004) to form a complete set on group theory