ENGLISH

Unitary symmetry and combinatorics

By James D. Louck

Book information

Publisher
World Scientific
Year
2008
ISBN
9812814728, 9789812814722
Open Library ID
OL23168273M
Language
english
Format
PDF
Filesize
3 MB (2949075 bytes)
Pages
619\642
Library
Kolxo3
Scanned
yes
Time added
2009-12-04 00:34:26

Description

This monograph integrates unitary symmetry and combinatorics, showing in great detail how the coupling of angular momenta in quantum mechanics is related to binary trees, trivalent trees, cubic graphs, MacMahon s master theorem, and other basic combinatorial concepts. A comprehensive theory of recoupling matrices for quantum angular momentum is developed. For the general unitary group, polynomial forms in many variables called matrix Schur functions have the remarkable property of giving all irreducible representations of the general unitary group and are the basic objects of study. The structure of these irreducible polynomials and the reduction of their Kronecker product is developed in detail, as is the theory of tensor operators. Contents: Quantum Angular Momentum; Composite Systems; Graphs and Adjacency Diagrams; Generating Functions; The D -Polynomials: Form; Operator Actions in Hilbert Space; The D-Polynomials: Structure; The General Linear and Unitary Groups; Tensor Operator Theory; Compendium A: Basic Algebraic Objects; Compendium B: Combinatorial Objects.

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