Symplectic Fibrations and Multiplicity Diagrams - Softcover

Guillemin, Victor

Softcover

ISBN 10: 0521111862 ISBN 13: 9780521111867

Publisher: Cambridge University Press, 2009

Synopsis

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.

About this title

Review

'The authors take a novel approach, using the techniques of symplectic geometry. They develop in detail some themes that were touched on in Symplectic Techniques in Physics (Guillemin and Sternberg, Cambridge University Press 1994).' L'Enseignement Mathématique

'The book contains a wealth of interesting material ... The book is a very interesting survey of a rapidly developing field of research and it is certainly worth of the effort needed to read and to understand it.' European Mathematical Society

Book Description

Multiplicity diagrams can be viewed as schemes for describing the phenomenon of 'symmetry breaking' in quantum physics. The authors take a novel approach, using the techniques of symplectic geometry, to the subject of multiplicity diagrams associated with the classical groups U(n), O(n), etc.

Edition details

• Publisher: Cambridge University Press
• Publication date: 2009
• ISBN 10: 0521111862
• ISBN 13: 9780521111867
• Binding: Paperback
• Language: English
• Edition number: 1
• Number of pages: 240