Lie algebras in particle physics /

Lie algebras in particle physics /

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Bibliographic Details
Author / Creator:Georgi, Howard.
Edition:2nd ed.
Imprint:Reading, Mass. : Perseus Books, Advanced Book Program, c1999.
Description:xviii, 320 p. : ill. ; 24 cm.
Language:English
Series:Frontiers in physics v. 54
Subject:
Lie algebras.
Particles (Nuclear physics)
S-matrix theory.
Lie algebras.
Particles (Nuclear physics)
S-matrix theory.
Format: Print Book
URL for this record:http://pi.lib.uchicago.edu/1001/cat/bib/4049962
Hidden Bibliographic Details
ISBN:0738202339
Notes:First edition was published in 1982 and has the subtitle: From isospin to unified theories. Subtitle appears on cover of this ed.
Includes bibliographical references and index.
Table of Contents:
  • Why Group Theory?
  • 1. Finite Groups
  • 1.1. Groups and representations
  • 1.2. Example - Z[subscript 3]
  • 1.3. The regular representation
  • 1.4. Irreducible representations
  • 1.5. Transformation groups
  • 1.6. Application: parity in quantum mechanics
  • 1.7. Example: S[subscript 3]
  • 1.8. Example: addition of integers
  • 1.9. Useful theorems
  • 1.10. Subgroups
  • 1.11. Schur's lemma
  • 1.12. * Orthogonality relations
  • 1.13. Characters
  • 1.14. Eigenstates
  • 1.15. Tensor products
  • 1.16. Example of tensor products
  • 1.17. * Finding the normal modes
  • 1.18. * Symmetries of 2n+1-gons
  • 1.19. Permutation group on n objects
  • 1.20. Conjugacy classes
  • 1.21. Young tableaux
  • 1.22. Example -- our old friend S[subscript 3]
  • 1.23. Another example -- S[subscript 4]
  • 1.24. * Young tableaux and representations of S[subscript n]
  • 2. Lie Groups
  • 2.1. Generators
  • 2.2. Lie algebras
  • 2.3. The Jacobi identity
  • 2.4. The adjoint representation
  • 2.5. Simple algebras and groups
  • 2.6. States and operators
  • 2.7. Fun with exponentials
  • 3. SU(2)
  • 3.1. J[subscript 3] eigenstates
  • 3.2. Raising and lowering operators
  • 3.3. The standard notation
  • 3.4. Tensor products
  • 3.5. J[subscript 3] values add
  • 4. Tensor Operators
  • 4.1. Orbital angular momentum
  • 4.2. Using tensor operators
  • 4.3. The Wigner-Eckart theorem
  • 4.4. Example
  • 4.5. * Making tensor operators
  • 4.6. Products of operators
  • 5. Isospin
  • 5.1. Charge independence
  • 5.2. Creation operators
  • 5.3. Number operators
  • 5.4. Isospin generators
  • 5.5. Symmetry of tensor products
  • 5.6. The deuteron
  • 5.7. Superselection rules
  • 5.8. Other particles
  • 5.9. Approximate isospin symmetry
  • 5.10. Perturbation theory
  • 6. Roots and Weights
  • 6.1. Weights
  • 6.2. More on the adjoint representation
  • 6.3. Roots
  • 6.4. Raising and lowering
  • 6.5. Lots of SU(2)s
  • 6.6. Watch carefully - this is important!
  • 7. SU(3)
  • 7.1. The Gell-Mann matrices
  • 7.2. Weights and roots of SU(3)
  • 8. Simple Roots
  • 8.1. Positive weights
  • 8.2. Simple roots
  • 8.3. Constructing the algebra
  • 8.4. Dynkin diagrams
  • 8.5. Example: G[subscript 2]
  • 8.6. The roots of G[subscript 2]
  • 8.7. The Cartan matrix
  • 8.8. Finding all the roots
  • 8.9. The SU(2)s
  • 8.10. Constructing the G[subscript 2] algebra
  • 8.11. Another example: the algebra C[subscript 3]
  • 8.12. Fundamental weights
  • 8.13. The trace of a generator
  • 9. More SU(3)
  • 9.1. Fundamental representations of SU(3)
  • 9.2. Constructing the states
  • 9.3. The Weyl group
  • 9.4. Complex conjugation
  • 9.5. Examples of other representations
  • 10. Tensor Methods
  • 10.1. Lower and upper indices
  • 10.2. Tensor components and wave functions
  • 10.3. Irreducible representations and symmetry
  • 10.4. Invariant tensors
  • 10.5. Clebsch-Gordan decomposition
  • 10.6. Triality
  • 10.7. Matrix elements and operators
  • 10.8. Normalization
  • 10.9. Tensor operators
  • 10.10. The dimension of (n,m)
  • 10.11. * The weights of (n,m)
  • 10.12. Generalization of Wigner-Eckart
  • 10.13. * Tensors for SU(2)
  • 10.14. * Clebsch-Gordan coefficients from tensors
  • 10.15. * Spin s[subscript 1] + s[subscript 2] - 1
  • 10.16. * Spin s[subscript 1] + s[subscript 2] - k
  • 11. Hypercharge and Strangeness
  • 11.1. The eight-fold way
  • 11.2. The Gell-Mann Okubo formula
  • 11.3. Hadron resonances
  • 11.4. Quarks
  • 12. Young Tableaux
  • 12.1. Raising the indices
  • 12.2. Clebsch-Gordan decomposition
  • 12.3. SU(3) [right arrow] SU(2) [times] U(1)
  • 13. SU(N)
  • 13.1. Generalized Gell-Mann matrices
  • 13.2. SU(N) tensors
  • 13.3. Dimensions
  • 13.4. Complex representations
  • 13.5. SU(N) [multiply sign in circle] SU(M) [set membership] SU(N +M)
  • 14. 3-D Harmonic Oscillator
  • 14.1. Raising and lowering operators
  • 14.2. Angular momentum
  • 14.3. A more complicated example
  • 15. SU(6) and the Quark Model
  • 15.1. Including the spin
  • 15.2. SU(N) [multiply sign in circle] SU(M) [set membership] SU(NM)
  • 15.3. The baryon states
  • 15.4. Magnetic moments
  • 16. Color
  • 16.1. Colored quarks
  • 16.2. Quantum Chromodynamics
  • 16.3. Heavy quarks
  • 16.4. Flavor SU(4) is useless!
  • 17. Constituent Quarks
  • 17.1. The nonrelativistic limit
  • 18. Unified Theories and SU(5)
  • 18.1. Grand unification
  • 18.2. Parity violation, helicity and handedness
  • 18.3. Spontaneously broken symmetry
  • 18.4. Physics of spontaneous symmetry breaking
  • 18.5. Is the Higgs real?
  • 18.6. Unification and SU(5)
  • 18.7. Breaking SU(5)
  • 18.8. Proton decay
  • 19. The Classical Groups
  • 19.1. The SO(2n) algebras
  • 19.2. The SO(2n + 1) algebras
  • 19.3. The Sp(2n) algebras
  • 19.4. Quaternions
  • 20. The Classification Theorem
  • 20.1. II-systems
  • 20.2. Regular subalgebras
  • 20.3. Other Subalgebras
  • 21. SO(2n + 1) and Spinors
  • 21.1. Fundamental weight of SO(2n + 1)
  • 21.2. Real and pseudo-real
  • 21.3. Real representations
  • 21.4. Pseudo-real representations
  • 21.5. R is an invariant tensor
  • 21.6. The explicit form for R
  • 22. SO(2n + 2) Spinors
  • 22.1. Fundamental weights of SO(2n + 2)
  • 23. SU(n) [subset or is implied by] SO(2n)
  • 23.1. Clifford algebras
  • 23.2. [Gamma][subscript m] and R as invariant tensors
  • 23.3. Products of [Gamma][subscript s]
  • 23.4. Self-duality
  • 23.5. Example: SO(10)
  • 23.6. The SU(n) subalgebra
  • 24. SO(10)
  • 24.1. SO(10) and SU(4) [times] SU(2) [times] SU(2)
  • 24.2. * Spontaneous breaking of SO(10)
  • 24.3. * Breaking SO(10) [right arrow] SU(5)
  • 24.4. * Breaking SO(10) [right arrow] SU(3) [times] SU(2) [times] U(1)
  • 24.5. * Breaking SO(10) [right arrow] SU(3) [times] U(1)
  • 24.6. * Lepton number as a fourth color
  • 25. Automorphisms
  • 25.1. Outer automorphisms
  • 25.2. Fun with SO(8)
  • 26. Sp(2n)
  • 26.1. Weights of SU(n)
  • 26.2. Tensors for Sp(2n)
  • 27. Odds and Ends
  • 27.1. Exceptional algebras and octonians
  • 27.2. E[subscript 6] unification
  • 27.3. Breaking E[subscript 6]
  • 27.4. SU(3) [times] SU(3) [times] SU(3) unification
  • 27.5. Anomalies
  • Epilogue
  • Index
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