The Application of Group Theory in Physics

The Application of Group Theory in Physics

1st Edition - January 1, 1960

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  • Author: G.Ya. Lyubarskii
  • eBook ISBN: 9781483225982

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Description

The Application of Group Theory in Physics is a 17-chapter text based on a course of lectures concerning the principles, concepts, and application of group theory in physics, given at the Gorki University in Kharkov. This text presents first the parts of the theory of representations of finite and continuous groups that are most important in application. Considerable chapters cover the groups of theory of interest in theoretical physics and demonstrate the principles according to which the abstract concepts and the theorems of representation theory are applied in theoretical physics. The remaining chapters provide representations of the rotation group and the Lorentz group. The closing part of this work contains tables of the detailed description of the 230 space groups and for the characters of certain groups. This book is intended primarily for physicists specializing in theoretical physics

Table of Contents


  • Preface

    Chapter I Elements of the Theory of Groups

    1. Groups

    2. Subgroups

    Isomorphism and Homomorphism of Groups

    Chapter II Some Specific Groups

    4. The Permutation Group

    5. The Rotation Group

    6. The Full Orthogonal Group

    7. The Euclidean Group

    8. The Point Groups

    9. The Point Groups of the First Kind

    10. The Point Groups of the Second Kind

    11. The Translation Group

    12. Syngonies

    13. The Symmetry of Crystals

    Chapter III The Theory of Group Representations

    14. Representation of a Group

    15. Equivalent Representations

    16. The Averaging Functional

    17. Reducible Representations

    18. Irreducible Representations and Orthogonality Properties

    19. The Completeness Theorem

    20. The Theory of Characters

    Chapter IV Operations with Group Representations

    21. The Product of Representations

    22. Conjugate Representation

    23. Real Representations

    24. The Direct Product

    25. Symmetrized Multiple Products of Representations

    26. Decomposition of a Reducible Representation into Irreducible Representations.

    Chapter V Representations of Certain Groups

    27. Representations of the Permutation Group Sn

    28. The Irreducible Representations of Point Groups

    29. Representations of Translation Groups

    30. Representations of Space Groups

    Chapter VI Small Oscillations of Symmetrical Systems

    31. Normal Coordinates and Eigen-Frequencies

    32. Symmetrical Coordinates

    33. The Lagrangian in Symmetrical Coordinates

    34. The Oscillatory Representation

    35. An Example: The Molecule CHC13(117)

    Chapter VII Second Order Phase Transitions

    36. Formulation of the problem

    37. Active Representations

    38. An Example

    Chapter VIII Crystals

    39. Sound in Crystals

    40. Electron Levels in a Crystal

    41. Tensors in Crystals

    Chapter IX Infinite Groups

    42. Specific Properties of Infinite Groups

    43. Elements of the Theory of Lie Groups

    44. Infinitesimal Representation of a Lie Group

    Chapter X Representations of the Rotation Groups in Two and Three Dimensions and of the Full Orthogonal Group

    45. The Irreducible Representations of the Two-dimensional Rotation Group Z

    46. Classification of the Irreducible Representations of Three-Dimensional Rotation Group

    47. The Matrix Elements of the Irreducible Representations

    48. Properties of the Irreducible Representations of the Rotation Group

    49. The Product of Representations of the Rotation Group

    50. Spinor Algebra

    51. Tensor Algebra

    52. Representations of the Full Orthogonal Group

    53. Double-Valued Representations of Point Groups

    Chapter XI Clebsch-Gordon and Racah Coefficients

    54. Evaluation of the Clebsch-Gordon Coefficients

    55. Properties of the Clebsch-Gordon Coefficients

    56. Racah Coeificients

    Chapter XII The Schrödinger Equation

    57. Conservation Laws

    58. Classification of States

    Chapter XIII Equations Invariant Under the Euclidean Group of Motions in Space

    59. Spherical Harmonics with Spin

    60. Equations Invariant Under the Group of Euclidean Motions in Space

    61. An Example

    Chapter XIV Absorption and Raman Scattering of Light

    62. Quantum Mechanical Introduction

    63. Selection Rules for the Absorption of Light by Atoms and Molecules

    64. Raman Scattering of Light by Atoms and Molecules

    Chapter XV Representations of the Lorentz Group

    65. The Lorentz Group

    66. Infinitesimal Operators of the Lorentz Group

    67. Classification of the Irreducible Representations of the Lorentz Group

    68. Product of Irreducible Representations of the Lorentz Group

    69. Complex-Conjugate Representations

    70. Spinor Algebra

    71. Tensor Algebra

    72. Representations of the Full Lorentz Group

    Chapter XVI Relativistically Invariant Equations

    73. The Wave Function

    74. Relativistically Invariant Equations

    75. The Lagrangiang

    76. Conservation Laws

    77. Spin

    78. The Relativistically Invariant Operation of Time Inversion and the Pauli Theorem

    79. The Dirac Equation

    Chapter XVII Nuclear Reactions

    80. The Scattering Matrix

    81. Angular Distribution of the Products of a Nuclear Reaction

    82. Angular Distribution of the Products of a Nuclear Reaction (Continued)

    Appendices

    I. Characters of Irreducible Representations of the Permutation Groups S4,S5,S6,S7.

    II. Characters of Irreducible Representations of Point Groups.

    III. Two-Valued Representations of Point Groups.

    IV. Space Groups.

    V. Racah Coefficients.

    Bibliography

    Subject Index

Product details

  • No. of pages: 392
  • Language: English
  • Copyright: © Pergamon 1960
  • Published: January 1, 1960
  • Imprint: Pergamon
  • eBook ISBN: 9781483225982

About the Author

G.Ya. Lyubarskii

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