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Symplectic fibrations and multiplicity diagrams

作者: Victor Guillemin; Eugene Lerman; Shlomo Sternberg
出版商: Cambridge ; New York : Cambridge University Press, 1996.
版本/格式:   Print book : 英語所有版本和格式的總覽
資料庫:WorldCat
提要:
"Multiplicity diagrams can be viewed as schemes for describing the phenomenon of "symmetry breaking" in quantum physics: Suppose the state space of a quantum mechanical system is a Hilbert space V, on which the symmetry group G of the system acts irreducibly. How does this Hilbert space break up when G gets replaced by a smaller symmetry group H? In the case where H is a maximal torus of a compact group a convenient
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資料類型: 網際網路資源
文件類型: 圖書, 網路資源
所有的作者/貢獻者: Victor Guillemin; Eugene Lerman; Shlomo Sternberg
ISBN: 0521443237 9780521443234
OCLC系統控制編碼: 33333376
描述: xiv, 222 pages : illustrations ; 24 cm
内容: 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 --
App. A. Multiplicity Formulas --
App. B. Equivariant Cohomology --
App. C. Update.
責任: Victor Guillemin, Eugene Lerman, Shlomo Sternberg.

摘要:

"Multiplicity diagrams can be viewed as schemes for describing the phenomenon of "symmetry breaking" in quantum physics: Suppose the state space of a quantum mechanical system is a Hilbert space V, on which the symmetry group G of the system acts irreducibly. How does this Hilbert space break up when G gets replaced by a smaller symmetry group H? In the case where H is a maximal torus of a compact group a convenient way to record the multiplicities is as integers drawn on the weight lattice of H."

"The subject of this book is the multiplicity diagrams associated with U(n), O(n), and the other classical groups. It presents such topics as asymptotic distributions of multiplicities, hierarchical patterns in multiplicity diagrams, lacunae, and the multiplicity diagrams of the rank-2 and rank-3 groups. 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 (V. Guillemin and S. Sternberg, Cambridge University Press, 1984), 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."--Jacket.

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