Symmetry Groups and Their Applications
Academic Press
Published on 2. March 1973
431 pages
978-0-08-087365-7 (ISBN)
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Symmetry Groups and Their Applications
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Willard Miller
Symmetry Groups and Their Applications
Book
01/1972
Academic Press
€121.95
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Content
- Front Cover
- SYMMETRY GROUPS AND THEIR APPLICATIONS
- Copyright Page
- Contents
- Preface
- Chapter 1. Elementary Group Theory
- 1.1 Abstract Groups
- 1.2 Subgroups and Cosets
- 1.3 Homomorphisms, Isomorphisms, and Automorphisms
- 1.4 Transformation Groups
- 1.5 New Groups from Old Ones
- Problems
- Chapter 2. The Crystallographic Groups
- 2.1 The Orthogonal Group in Three-Space
- 2.2 The Euclidean Group
- 2.3 Symmetry and the Discrete Subgroups of E(3)
- 2.4 Point Groups of the First Kind
- 2.5 Point Groups of the Second Kind
- 2.6 Lattice Groups
- 2.7 Crystallographic Point Groups
- 2.8 The Bravais Lattices
- 2.9 Crystal Structure
- 2.10 Space Groups
- Problems
- Chapter 3. Group Representation Theory
- 3.1 A Group Representation
- 3.2 Reducible Representations
- 3.3 Irreducible Representations
- 3.4 Group Characters
- 3.5 New Representations from Old Ones
- 3.6 Character Tables
- 3.7 The Method of Projection Operators
- 3.8 Applications
- Problems
- Chapter 4. Representations of the Symmetric Groups
- 4.1 Conjugacy Classes in Sn
- 4.2 Young Tableaux
- 4.3 Symmetry Classes of Tensors
- 4. 4 The Simple Characters of Sa
- Problems
- Chapter 5. Lie Groups and Lie Algebras
- 5.1 The Exponential of a Matrix
- 5.2 Local Lie Groups
- 5.3 Lie Algebras
- 5.4 The Classical Groups
- 5.5 The Exponential Map of a Lie Algebra
- 5.6 Local Homomorphisms and Isomorphisms
- 5.7 Subgroups and Subalgebras
- 5.8 Representations of Lie Groups
- 5.9 Local Transformation Groups
- 5.10 Examples of Transformation Groups
- Problems
- Chapter 6. Compact Lie Groups
- 6.1 Invariant Measures on Lie Groups
- 6.2 Compact Linear Lie Groups
- 6.3 Group Characters and Representations
- Problems
- Chapter 7. The Rotation Group and Its Representations
- 7.1 The Groups SO(3) and SU(2)
- 7.2 Irreducible Representations of SU(2)
- 7.3 Irreducible Representations of sl ( 2 )
- 7.4 Expansion Theorems for Functions on SU(2)
- 7.5 New Realizations of the Irreducible Representations
- 7.6 Applications to Physics
- 7.7 The Clebsch-Gordan Coefficients
- 7.8 Applications of the Clebsch-Gordan Series
- 7.9 Double-Valued Representations of the Crystallographic Groups
- 7.10 The Wigner-Eckart Theorem and Its Applications
- 7.11 Spinor Fields and Invariant Equations
- Problems
- Chapter 8. The Lorentz Group and Its Representations
- 8.1 The Homogeneous Lorentz Group
- 8.2 The Physical Significance of Lorentz Invariance
- 8.3 Representations of the Lorentz Group
- 8.4 Models of the Representations
- 8.5 Lorentz-Invariant Equations
- Problems
- Chapter 9. Representations of the Classical Groups
- 9.1 Representations of the General Linear Groups
- 9.2 Character Formulas
- 9.3 The Irreducible Representations of GL(m, R), SL(m, E), and SU(m)
- 9.4 The Symplectic Groups and Their Representations
- 9.5 The Orthogonal Groups and Their Representations
- 9.6 Dirac Matrices and the Spin Representations of the Orthogonal Groups
- 9.7 Examples and Applications
- 9.8 The Pauli Exclusion Principle and the Periodic Table
- 9.9 The Group Ring Revisited
- 9.10 Semisimple Lie Algebras
- Problems
- Chapter 10. The Harmonic Oscillator Group
- 10.1 The Harmonic Oscillator
- 10.2 Representations of the Harmonic Oscillator Group
- Problems
- Appendix. Hilbert Space
- References
- Symbol Index
- Index
