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


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