An Introduction to Groups and their Matrices for Science Students

This text for advanced undergraduates develops group theory from triangle symmetry to particle physics, supported by examples from research.

Robert Kolenkow (Author)

9781108831086, Cambridge University Press

Hardback, published 2 June 2022

360 pages
26.2 x 18.5 x 2.3 cm, 0.81 kg

Group theory, originating from algebraic structures in mathematics, has long been a powerful tool in many areas of physics, chemistry and other applied sciences, but it has seldom been covered in a manner accessible to undergraduates. This book from renowned educator Robert Kolenkow introduces group theory and its applications starting with simple ideas of symmetry, through quantum numbers, and working up to particle physics. It features clear explanations, accompanying problems and exercises, and numerous worked examples from experimental research in the physical sciences. Beginning with key concepts and necessary theorems, topics are introduced systematically including: molecular vibrations and lattice symmetries; matrix mechanics; wave mechanics; rotation and quantum angular momentum; atomic structure; and finally particle physics. This comprehensive primer on group theory is ideal for advanced undergraduate topics courses, reading groups, or self-study, and it will help prepare graduate students for higher-level courses.

1. Fundamental concepts
2. Matrix representations of discrete groups
3. Molecular vibrations
4. Crystalline solids
5. Bohr's quantum theory and matrix mechanics
6. Wave mechanics, measurement, and entanglement
7. Rotation
8. Quantum angular momentum
9. The structure of atoms
10. Particle physics. Appendices.

Subject Areas: Physics [PH], Applied mathematics [PBW], Algebra [PBF]