Lie Groups for Pedestrians (eBook)

Preface to first edition Preface to second edition1. Introduction 1.1 Review of angular momentum algebra 1.2 Generalization by analogy of the angular momentum results 1.3 Properties of bilinear products of second quantized creation and annihilation operators2. Isospin. A simple example 2.1 The Lie algebra 2.2 The use of isospin in physical problems 2.3 The relation between isospin invariance and charge independence 2.4 The use of the group theoretical method3. The group SU subscript 3 and its application to elementary particles 3.1 The Lie algebra 3.2 The structure of the multiplets 3.3 Combining SU subscript 3 multiplets 3.4 R-symmetry and charge conjugation 3.5 The generalization to any SU subscript 3 algebra 3.6 The octet model of elementary particles 3.7 The most general SU subscript 3 classification4. The three-dimensional harmonic oscillator 4.1 The quasispin classification 4.2 The angular momentum classification 4.3 Systems of several harmonic oscillators 4.4 The Elliott model5. Algebras of operators which change the number of particles 5.1 Pairing quasispins 5.2 Identification of the Lie algebra 5.3 Seniority 5.4 Symplectic groups 5.5 Seniority with neutrons and protons. The group Sp subscript 4 5.6 Lie algebras of boson operators. Non-compact groups 5.7 The general classification of Lie algebras of bilinear products6. Permutations, bookkeeping and young diagrams7. The groups SU subscript 4, SU subscript 6 and SU subscript 12, an introduction to groups of higher rank 7.1 The group SU subscript 4 and its classification with an SU subscript 3 subgroup 7.2 The SU subscript 2 xSU subscript 2 multiplet structure of SU subscript 4 7.3 The Wigner supermultiplet SU subscript 4 7.4 The group SU subscript 6 7.5 The group SU subscript 12Appendix A. Construction of the SU subscript 3 multiplets by combining sakaton tripletsAppendix B. Calculations of SU subscript 3 using an SU subscript 2 subgroup: U-spinAppendix C. Experimental predictions from the octet model of unitary symmetryAppendix D. Phases, a perennial headache Bibliography Subject Index