Applications of Finite Groups - 1st Edition - ISBN: 9781483231327, 9781483268965

Applications of Finite Groups

1st Edition

Authors: J. S. Lomont
eBook ISBN: 9781483268965
Imprint: Academic Press
Published Date: 1st January 1959
Page Count: 358
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Description

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.

Table of Contents


Preface


List of Symbols


I. Matrices


II. Groups


1. Abstract Properties


2. Applications


A. Thermodynamics


B. The Dirac Equation


C. Fermion Annihilation and Creation Operators


III. Representations


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


IV. Applications


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


Details

No. of pages:
358
Language:
English
Copyright:
© Academic Press 1959
Published:
Imprint:
Academic Press
eBook ISBN:
9781483268965

About the Author

J. S. Lomont

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