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Applications of Finite Groups focuses on the applications of finite groups to problems of physics, including representation theory, crystals, wave equations, and nuclear and molecular structures.
The book first elaborates on matrices, groups, and representations. Topics include abstract properties, applications, matrix groups, key theorem of representation theory, properties of character tables, simply reducible groups, tensors and invariants, and representations generated by functions. The text then examines applications and subgroups and representations, as well as subduced and induced representations, fermion annihilation and creation operators, crystallographic point groups, proportionality tensors in crystals, and nonrelativistic wave equations.
The publication takes a look at space group representations and energy bands, symmetric groups, and applications. Topics include molecular and nuclear structures, multiplet splitting in crystalline electric fields, construction of irreducible representations of the symmetric groups, and reality of representations.
The manuscript is a dependable source of data for physicists and researchers interested in the applications of finite groups.
List of Symbols
1. Abstract Properties
B. The Dirac Equation
C. Fermion Annihilation and Creation Operators
1. Matrix Groups
2. The Key Theorem of Representation Theory
3. Character Tables
4. Computation of Character Tables
5. Properties of Character Tables
6. Faithful Representations
7. Kronecker Products
8. Simply Reducible Groups
9. Reduction by Idempotents
10. Groups of Mathematical Physics
A. Cyclic Groups
B. Dihedral Groups
C. Tetrahedral Group
D. Octahedral Group
E. Icosahedral Group
11. Tensors and Invariants
12. Representations Generated by Functions
13. Subduced Representations
1. Fermion Annihilation and Creation Operators
2. Molecular Vibrations (Classical)
3. Symmetric Waveguide Junctions
4. Crystallographic Point Groups
5. Proportionality Tensors in Crystals
6. The Three-Dimensional Rotation Group
7. Double Point Groups
8. Nonrelativistic Wave Equations
9. Stationary Perturbation Theory
10. Lattice Harmonics
11. Molecular Orbitals
12. Crystallographic Lattices
13. Crystallographic Space Groups
14. Wave Functions in Crystals
V. Subgroups and Representations
1. Subduced Representations
2. Induced Representations
3. Induced and Subduced Representations
4. Projective Representations
5. Little Groups
VI. Space Group Representations and Energy Bands
1. Representation Theory
2. Example—Two-Dimensional Square Lattice
3. Reality of Representations
VII. Symmetric Groups
1. Abstract Properties of ℓ(n)
2. Representations of ℓ(n)
3. Miscellany and the Full Linear Groups
4. Construction of Irreducible Representations of the Symmetric Groups
1. Permutation Degeneracy and the Pauli Exclusion Principle
2. Atomic Structure
A. The Central Field Approximation
B. LS Coupling
3. Multiplet Splitting in Crystalline Electric Fields
4. Molecular Structure
5. Nuclear Structure
A. Spatial Coordinate Approximation
B. Spin Approximation
6. Selection Rules
Appendix I: Proof of the Key Theorem of Representation Theory
Appendix II: Irreducible Representations of D3, D4, D6, T, O, and I
Appendix III: The Lorentz Groups
- No. of pages:
- © Academic Press 1959
- 1st January 1959
- Academic Press
- eBook ISBN:
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