Synopses & Reviews
This self-contained text presents a consistent description of the geometric and quaternionic treatment of rotation operators, employing methods that lead to a rigorous formulation and offering complete solutions to many illustrative problems.
Geared toward upper-level undergraduates and graduate students, the book begins with chapters covering the fundamentals of symmetries, matrices, and groups, and it presents a primer on rotations and rotation matrices. Subsequent chapters explore rotations and angular momentum, tensor bases, the bilinear transformation, projective representations, and the geometry, topology, and algebra of rotations. Some familiarity with the basics of group theory is assumed, but the text assists students in developing the requisite mathematical tools as necessary.
Synopsis
This self-contained text presents a consistent description of the geometric and quaternionic treatment of rotation operators, employing methods that lead to a rigorous formulation and offering complete solutions to the many illustrative problems. Geared toward upper-level undergraduates and graduate students, it begins with chapters covering the fundamentals of symmetries, matrices, and groups and presenting a primer on rotations and rotation matrices. Subsequent chapters explore rotations and angular momentum, tensor bases, the bilinear transformation, projective representations, and the geometry, topology, and algebra of rotations. 336pp. 63 illustrations. 53/8 x 81/2.
Synopsis
This text presents a consistent description of the geometric and quaternionic treatment of rotation operators. Covers the fundamentals of symmetries, matrices, and groups and presents a primer on rotations and rotation matrices. Also explores rotations and angular momentum, tensor bases, the bilinear transformation, projective representations, more. Includes problems with solutions.
Table of Contents
0. Notation. Conventions. How to Use This Book
1. Introduction
2. All You Need to Know about Symmetries, Matrices, and Groups
3. A Primer on Rotations and Rotation Matrices
4. Rotations and Angular Momentum
5. Tensor Bases: Introduction to Spinors
6. The Bilinear Transformation
7. Rotations and SU(2). The Stereographic Projection
8. Projective Representations
9. The Geometry of Rotations
10. The Topology of Rotations
11. The Spinor Representations
12. The Algebra of Rotations: Quaternions
13. Double Groups
14. The Irreducible Representations of SO(3)
15. Examples and Applications
16. Solutions to Problems
References
Index