Book:Harry J. Lipkin/Lie Groups for Pedestrians/Second Edition
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Harry J. Lipkin: Lie Groups for Pedestrians (2nd Edition)
Published $\text {1966}$, Dover Publications
- ISBN 0-486-45326-X
Subject Matter
Contents
- Preface to First Edition
- Preface to Second Edition
- Chapter $1$ 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 operators
- Chapter $2$ 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 method
- Chapter $3$ The Group $\SU 3$ and its Application to Elementary Particles
- $\$ 3.1$. The Lie algenra
- $\$ 3.2$. The structure of the multiplets
- $\$ 3.3$. Combining $\SU 2$ multiplets
- $\$ 3.4$. $R$-symmetry and charge conjugation
- $\$ 3.5$. The generalization to any $\SU 3$ algebra
- $\$ 3.6$. The octet model of elementary particles
- $\$ 3.7$. The most general $\SU 3$ classification
- Chapter $4$ 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 method
- Chapter $5$ 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 $\mathrm {Sp}_4$
- $\$ 5.6$. Lie algebras of boson operators. Non-compact groups
- $\$ 5.7$. The general classification of Lie algebras of bilinear products
- Chapter $6$ Permutations, Bookkeeping and Young Diagrams
- Chapter $7$ The Groups $\SU 4$, $\SU 6$ and $\SU {12}$, an Introduction to Groups of Higher Rank
- $\$ 7.1$. The group $\SU 4$ and its classification with an $\SU 3$ subgroup
- $\$ 7.2$. The $\SU 2 \times \SU 2$ multiplet structure of $\SU 4$
- $\$ 7.3$. The Wigner supermultiplet $\SU 4$
- $\$ 7.4$. The group $\SU 6$
- $\$ 7.5$. The group $\SU {12}$
- Appendices
- a. Construction of the $\SU 3$ multiplets by combining sakaton triplets
- b. Calculations of $\SU 3$ using an $\SU 2$ subgroup: $U$-spin
- c. Experimental predictions from the octet model of unitary symmetry
- d. Phases, a perennial headache
- Bibliography
- Subject Index
Further Editions
Source work progress
- 1966: Harry J. Lipkin: Lie Groups for Pedestrians (2nd ed.): $\S 1$: Introduction