Group Theory and the Interaction of Composite Nucleon Systems [Paperback]

1 Introduction.- 2 Permutational Structure of Nuclear States.- 2.1 Concepts and Motivation.- 2.2 The Symmetric Group S(n).- 2.3 Irreducible Representations of the Symmetric Group S(n).- 2.4 Construction of States of Orbital Symmetry, Young Operators.- 2.5 Computation of Irreducible Representations of the Symmetric Group.- 2.6 Spin, Isospin and the Supermultiplet Scheme.- 2.7 Matrix Elements in the Supermultiplet Scheme.- 2.8 Supermultiplet Expansion for States of Light Nuclei.- 2.9 Notes and References.- 3 Unitary Structure of Orbital States.- 3.1 Concepts and Motivation.- 3.2 The General Linear and the Unitary Group and Their Finite-Dimensional Representations.- 3.3 Wigner Coefficients of the Group GL(j, C).- 3.4 Computation of Irreducible Representations of GL(j, C) from Double Gelfand Polynomials.- 3.5 Computation of Irreducible Representations of GL(j,C) from Representations of the Symmetric Group S (n).- 3.6 Conjugation Relations of Irreducible Representations of GL (j, C).- 3.7 Fractional Parentage Coefficients and Their Computation.- 3.8 Bordered Decomposition of Irreducible Representations for the Group GL(j, C).- 3.9 Orbital Configurations of n Particles.- 3.10 Decomposition of Orbital Matrix Elements.- 3.11 Orbital Matrix Elements for the Configuration f = [4j].- 3.12 Notes and References.- 4 Geometric Transformations in Classical Phase Space and their Representation in Quantum Mechanics.- 4.1 Concepts and Motivation.- 4.2 Symplectic Geometry of Classical Phase Space.- 4.3 Basic Structure of Bargmann Space.- 4.4 Representation of Translations in Phase Space by Weyl Operators.- 4.5 Representation of Linear Canonical Transformations.- 4.6 Oscillator States of a Single Particle with Angular Momentum and Matrix Elements of Some Operators.- 4.7 Notes and References.- 5 Linear Canonical Transformations and Interacting n-particle Systems.- 5.1 Orthogonal Point Transformations in n-particle Systems and their Representations.- 5.2 General Linear Canonical Transforml³;