Front Cover -- Group Theory in Physics: An Introduction -- Copyright Page -- Contents -- Preface -- Chapter 1. The Basic Framework -- 1. The concept of a group -- 2. Groups of coordinate transformations -- 3. The group of the Schrödinger equation -- 4. The role of matrix representations -- Chapter 2. The Structure of Groups -- 1. Some elementary considerations -- 2. Classes -- 3. Invariant subgroups -- 4. Cosets -- 5. Factor groups -- 6. Homomorphic and isomorphic mappings -- 7. Direct products and semi-direct products of groups -- Chapter 3. Lie Groups -- 1. Definition of a linear Lie group -- 2. The connected components of a linear Lie group -- 3. The concept of compactness for linear Lie -- 4. Invariant integration -- Chapter 4. Representations of Groups - Principal Ideas -- 1. Definitions -- 2. Equivalent representations -- 3. Unitary representations -- 4. Reducible and irreducible representations -- 5. Schur's Lemmas and the orthogonality theorem for matrix representations -- 6. Characters -- Chapter 5. Representations of Groups - Developments -- 1. Projection operators -- 2. Direct product representations -- 3. The Wigner-Eckart Theorem for groups of coordinate transfor-mations in IR3 -- 4. The Wigner-Eckart Theorem generalized -- 5. Representations of direct product groups -- 6. Irreducible representations of finite Abelian groups -- 7. Induced representations -- Chapter 6. Group Theory in Quantum Mechanical Calculations -- 1. The solution of the Schrödinger equation -- 2. Transition probabilities and selection rules -- 3. Time-independent perturbation theory -- Chapter 7. Crystallographic Space Groups -- 1. The Bravais lattices -- 2. The cyclic boundary conditions -- 3. Irreducible representations of the group T of pure primitive translations and Bloch's Theorem -- 4. Brillouin zones -- 5. Electronic energy bands.

6. Survey of the crystallographic space groups -- 7. Irreducible representations of symmorphic space groups -- 8. Consequences of the fundamental theorems -- Chapter 8. The Role of Lie Algebras -- 1. "Local" and "global" aspects of Lie groups -- 2. The matrix exponential function -- 3. One-parameter subgroups -- 4. Lie algebras -- 5. The real Lie algebras that correspond to general linear Lie groups -- Chapter 9. The Relationships between Lie Groups and Lie Algebras Explored -- 1. Introduction -- 2. Subalgebras of Lie algebras -- 3. Homomorphic and isomorphic mappings of Lie algebras -- 4. Representations of Lie algebras -- 5. The adjoint representations of Lie algebras and linear Lie groups -- 6. Direct sum of Lie algebras -- Chapter 10. The Three-dimensional Rotation Groups -- 1. Some properties reviewed -- 2. The class structures of SU(2) and SO(3) -- 3. Irreducible representations of the Lie algebras su(2) and so(3) -- 4. Representations of the Lie groups SU(2), SO(3) and O(3) -- 5. Direct products of irreducible representations and the Clebsch-Gordan coefficients -- 6. Applications to atomic physics -- Chapter 11. The Structure of Semi-simple Lie Algebras -- 1. An outline of the presentation -- 2. The Killing form and Cartan's criterion -- 3. Complexification -- 4. The Cartan subalgebras and roots of semi-simple complex Lie algebras -- 5. Properties of roots of semi-simple complex Lie algebras -- 6. The remaining commutation relations -- 7. The simple roots -- 8. The Weyl canonical form of L -- 9. The Weyl group of L -- 10. Semi-simple real Lie algebras -- Chapter 12. Representations of Semi-simple Lie Algebras -- 1. Some basic ideas -- 2. The weights of a representation -- 3. The highest weight of a representation -- 4. The irreducible representations of L = A2, the complexification of L = su(3) -- 5. Casimir operators.

Chapter 13. Symmetry schemes for the elementary particles -- 1. Leptons and hadrons -- 2. The global internal symmetry group SU(2) and isotopic spin -- 3. The global internal symmetry group SU(3) and strangeness -- APPENDICES -- Appendix A. Matrices -- 1. Definitions -- 2. Eigenvalues and eigenvectors -- Appendix B. Vector Spaces -- 1. The concept of a vector space -- 2. Inner product spaces -- 3. Hilbert spaces -- 4. Linear operators -- 5. Bilinear forms -- 6. Linear functionals -- 7. Direct product spaces -- Appendix C. Character Tables for the Crystallographic Point Groups -- D. Properties of the Classical Simple Complex Lie Algebras -- 1. The simple complex lie algebra Al, l ≥ 1 -- 2. The simple complex Lie algebra Bl, l ≥ 1 -- 3. The simple complex Lie algebra Cl, 1 ≥ 1 -- 4. The simple complex Lie algebra D1, 1 ≥ 3 (and the semi-simple complex Lie algebra D2) -- References -- Index.