Title: Group theory and physics /
Authors: Sternberg, Shlomo.
Publisher: Cambridge University Press,
Year: 1994
Subjects: Group theory; Mathematical physics.
Contents: 1. Basic definitions and examples. 1.1. Groups: definition and examples. 1.2. Homomorphisms: the relation between SL(2,C) and the Lorentz group. 1.3. The action of a group on a set. 1.4. Conjugation and conjugacy classes. 1.5. Applications to crystallography. 1.6. The topology of SU(2) and SO(3). 1.7. Morphisms. 1.8. The classification of the finite subgroups of SO(3). 1.9. The classification of the finite subgroups of O(3). 1.10. The icosahedral group and the fullerenes -- 2. Representation theory of finite groups. 2.1. Definitions, examples, irreducibility. 2.2. Complete reducibility. 2.3. Schur's lemma. 2.4. Characters and their orthogonality relations. 2.5. Action on function spaces. 2.6. The regular representation. 2.7. Character tables. 2.8. The representations of the symmetric group -- 3. Molecular vibrations and homogeneous vector bundles. 3.1. Small oscillations and group theory. 3.2. Molecular displacements and vector bundles. 3.3. Induced representations. 3.4. Principal bundles.