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"This book is aimed at graduate students in physics who are studying group theory and its application to physics. It contains a short explanation of the fundamental knowledge and method, and the fundamental exercises for the method, as well as some important conclusions in group theory." &...

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Detalles Bibliográficos
Clasificación:Libro Electrónico
Autor principal: Ma, Zhongqi, 1940-
Otros Autores: Gu, X. Y. (Xiao-Yan)
Formato: Electrónico eBook
Idioma:Inglés
Publicado: River Edge, N.J. : World Scientific, ©2004.
Temas:
Group theory.
Mathematical physics.
Théorie des groupes.
Physique mathématique.
SCIENCE > Physics > Mathematical & Computational.
Group theory
Mathematical physics
Acceso en línea:Texto completo
Tabla de Contenidos:
  • Cover
  • Contents
  • Preface
  • 1. REVIEW ON LINEAR ALGEBRAS
  • 1.1 Eigenvalues and Eigenvectors of a Matrix
  • 1.2 Some Special Matrices
  • 1.3 Similarity Transformation
  • 2. GROUP AND ITS SUBSETS
  • 2.1 Definition of a Group
  • 2.2 Subsets in a Group
  • 2.3 Homomorphism of Groups
  • 3. THEORY OF REPRESENTATIONS
  • 3.1 Transformation Operators for a Scalar Function
  • 3.2 Inequivalent and Irreducible Representations
  • 3.3 Subduced and Induced Representations
  • 3.4 The Clebsch-Gardan Coefficients
  • 4. THREE-DIMENSIONAL ROTATION GROUP
  • 4.1 SO(3) Group and Its Covering Group SU(2)
  • 4.2 Inequivalent and Irreducible Representations
  • 4.3 Lie Groups and Lie Theorems
  • 4.4 Irreducible Tensor Operators
  • 4.5 Unitary Representations with Infinite Dimensions
  • 5. SYMMETRY OF CRYSTALS
  • 5.1 Symmetric Operations and Space Groups
  • 5.2 Symmetric Elements
  • 5.3 International Notations for Space Groups
  • 6. PERMUTATION GROUPS
  • 6.1 Multiplication of Permutations
  • 6.2 Young Patterns, Young Tableaux and Young Operators
  • 6.3 Primitive Idempotents in the Group Algebra
  • 6.4 Irreducible Representations and Characters
  • 6.5 The Inner and Outer Products of Representations
  • 7. LIE GROUPS AND LIE ALGEBRAS
  • 7.1 Classification of Semisimple Lie Algebras
  • 7.2 Irreducible Representations and the Chevalley Bases
  • 7.3 Reduction of the Direct Product of Representations
  • 8. UNITARY GROUPS
  • 8.1 The SU(N) Group and Its Lie Algebra
  • 8.2 Irreducible Tensor Representations of SU(N)
  • 8.3 Orthonormal Bases for Irreducible Representations
  • 8.4 Subduced Representations
  • 8.5 Casimir Invariants of SU(N)
  • 9. REAL ORTHOGONAL GROUPS
  • 9.1 Tensor Representations of SO(N)
  • 9.2 Spinor Representations of SO(N)
  • 9.3 SO(4) Group and the Lorentz Group
  • 10. THE SYMPLECTIC GROUPS
  • 10.1 The Groups Sp(2l, R) and USp(2l)
  • 10.2 Irreducible Representations of Sp(2l)
  • Bibliography
  • Index.

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