The Application of Group Theory in Physics

1st Edition - January 1, 1960
Author: G.Ya. Lyubarskii
Language: English
eBook ISBN:
9 7 8 - 1 - 4 8 3 2 - 2 5 9 8 - 2

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… Read more

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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

PrefaceChapter I Elements of the Theory of Groups 1. Groups 2. Subgroups Isomorphism and Homomorphism of GroupsChapter 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 CrystalsChapter 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 CharactersChapter 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 GroupsChapter 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 ExampleChapter VIII Crystals 39. Sound in Crystals 40. Electron Levels in a Crystal 41. Tensors in CrystalsChapter IX Infinite Groups 42. Specific Properties of Infinite Groups 43. Elements of the Theory of Lie Groups 44. Infinitesimal Representation of a Lie GroupChapter 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 GroupsChapter XI Clebsch-Gordon and Racah Coefficients 54. Evaluation of the Clebsch-Gordon Coefficients 55. Properties of the Clebsch-Gordon Coefficients 56. Racah CoeificientsChapter XII The Schrödinger Equation 57. Conservation Laws 58. Classification of StatesChapter 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 ExampleChapter 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 MoleculesChapter 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 GroupChapter 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 EquationChapter 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.BibliographySubject Index