Description
CAMBRIDGE Symplectic Fibrations and Multiplicity Diagrams 2009 Edition by Victor Guillemin, Eugene Lerman, Shlomo Sternberg
Multiplicity diagrams can be viewed as schemes for describing the phenomenon of 'symmetry breaking' in quantum physics. The subject of this book is the multiplicity diagrams associated with the classical groups U(n), O(n), etc. It presents such topics as asymptotic distributions of multiplicities, hierarchical patterns in multiplicity diagrams, lacanae, and the multiplicity diagrams of the rank 2 and rank 3 groups. The authors take a novel approach, using the techniques of symplectic geometry. The book develops in detail some themes which were touched on in the highly successful Symplectic Techniques in Physics by V. Guillemin and S. Sternberg, including the geometry of the moment map, the Duistermaat-Heckman theorem, the interplay between coadjoint orbits and representation theory, and quantization. Students and researchers in geometry and mathematical physics will find this book fascinating. Table of contents :- 1. Symplectic fibrations; 2. Examples of symplectic fibrations: the coadjoint orbit hierarchy; 3. Duistermaat-Heckman polynomials; 4. Symplectic fibrations and multiplicity diagrams; 5. Computations with orbits; Appendices; Bibliography; Index.