Lie Groups for Pedestrians [NOOK Book]

Overview


According to the author of this concise, high-level study, physicists often shy away from group theory, perhaps because they are unsure which parts of the subject belong to the physicist and which belong to the mathematician. However, it is possible for physicists to understand and use many techniques which have a group theoretical basis without necessarily understanding all of group theory. This book is designed to familiarize physicists with those techniques. Specifically, the author aims to show how the ...

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Lie Groups for Pedestrians

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Overview


According to the author of this concise, high-level study, physicists often shy away from group theory, perhaps because they are unsure which parts of the subject belong to the physicist and which belong to the mathematician. However, it is possible for physicists to understand and use many techniques which have a group theoretical basis without necessarily understanding all of group theory. This book is designed to familiarize physicists with those techniques. Specifically, the author aims to show how the well-known methods of angular momentum algebra can be extended to treat other Lie groups, with examples illustrating the application of the method.
Chapters cover such topics as a simple example of isospin; the group SU3 and its application to elementary particles; the three-dimensional harmonic oscillator; algebras of operators which change the number of particles; permutations; bookkeeping and Young diagrams; and the groups SU4, SU6, and SU12, an introduction to groups of higher rank. Four appendices provide additional valuable data.

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Editorial Reviews

From The Critics
This guide, a reprint of a 1966 work (itself a second edition of a 1965 work, North-Holland Publishing), is for physicists who want to familiarize themselves with algebraic techniques that have their basis in group theory. Lipkin (The Weizmann Institute of Science, Israel) describes how the well-known techniques of angular momentum algebra can be extended to treat other Lie groups and gives several examples illustrating the application of the method. The appendices present a detailed study of the application of SU3 algebra to unitary symmetry of elementary particles. Annotation c. Book News, Inc., Portland, OR
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Product Details

  • ISBN-13: 9780486137889
  • Publisher: Dover Publications
  • Publication date: 5/11/2012
  • Series: Dover Books on Physics
  • Sold by: Barnes & Noble
  • Format: eBook
  • Pages: 192
  • File size: 5 MB

Table of Contents

Preface to first edition
Preface to second edition
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
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
3. 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 classification
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 model
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 Sp subscript 4
5.6 Lie algebras of boson operators. Non-compact groups
5.7 The general classification of Lie algebras of bilinear products
6. Permutations, bookkeeping and young diagrams
7. 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 12
Appendix A. Construction of the SU subscript 3 multiplets by combining sakaton triplets
Appendix B. Calculations of SU subscript 3 using an SU subscript 2 subgroup: U-spin
Appendix C. Experimental predictions from the octet model of unitary symmetry
Appendix D. Phases, a perennial headache
Bibliography
Subject Index
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