Synopses & Reviews
The geometric approach to quantization was introduced by Konstant and Souriau more than 20 years ago. It has given valuable and lasting insights into the relationship between classical and quantum systems, and continues to be a popular research topic. The ideas have proved useful in pure mathematics, notably in representation theory, as well as in theoretical physics. The most recent applications have been in conformal field theory and in the Jones-Witten theory of knots. The successful original edition of this book was published in 1980. Now it has been completely revised and extensively rewritten. The presentation has been simplified and many new examples have been added. The material on field theory has been expanded.
Review
"Revised to simplify the presentation, provide additional examples, and correct errors in the First Edition." --American Mathematical Monthly
". . . the second edition clearly contains much that is new; in addition, the old material has been substantially rewritten and reorganized . . . . the arrangement of topics has been altered, so as to produce a more natural development from classical to quantum . . . . an attractive presentation of a dynamic subject." --P.L. Robinson, Mathematical Reviews
Table of Contents
1. Symplectic Geometry
2. Lagrangian and Hamiltonian Mechanics
3. Symmetry
4. Hamilton-Jacobi Theory
5. Complex Polarizations
6. Elementary Relativistic Systems
7. Classical Fields
8. Prequantization
9. Quantization
10. The Metaplectic Correction