UID:
almafu_9958090988802883
Umfang:
1 online resource (445 p.)
ISBN:
1-281-76868-5
,
9786611768683
,
0-08-087365-0
Serie:
Pure and applied mathematics; a series of monographs and textbooks ; v. 50
Inhalt:
Symmetry groups and their applications
Anmerkung:
Description based upon print version of record.
,
Front Cover; SYMMETRY GROUPS AND THEIR APPLICATIONS; Copyright Page; Contents; Preface; Chapter 1. Elementary Group Theory; 1.1 Abstract Groups; 1.2 Subgroups and Cosets; 1.3 Homomorphisms, Isomorphisms, and Automorphisms; 1.4 Transformation Groups; 1.5 New Groups from Old Ones; Problems; Chapter 2. The Crystallographic Groups; 2.1 The Orthogonal Group in Three-Space; 2.2 The Euclidean Group; 2.3 Symmetry and the Discrete Subgroups of E(3); 2.4 Point Groups of the First Kind; 2.5 Point Groups of the Second Kind; 2.6 Lattice Groups; 2.7 Crystallographic Point Groups; 2.8 The Bravais Lattices
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2.9 Crystal Structure2.10 Space Groups; Problems; Chapter 3. Group Representation Theory; 3.1 A Group Representation; 3.2 Reducible Representations; 3.3 Irreducible Representations; 3.4 Group Characters; 3.5 New Representations from Old Ones; 3.6 Character Tables; 3.7 The Method of Projection Operators; 3.8 Applications; Problems; Chapter 4. Representations of the Symmetric Groups; 4.1 Conjugacy Classes in Sn; 4.2 Young Tableaux; 4.3 Symmetry Classes of Tensors; 4. 4 The Simple Characters of Sa; Problems; Chapter 5. Lie Groups and Lie Algebras; 5.1 The Exponential of a Matrix
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5.2 Local Lie Groups5.3 Lie Algebras; 5.4 The Classical Groups; 5.5 The Exponential Map of a Lie Algebra; 5.6 Local Homomorphisms and Isomorphisms; 5.7 Subgroups and Subalgebras; 5.8 Representations of Lie Groups; 5.9 Local Transformation Groups; 5.10 Examples of Transformation Groups; Problems; Chapter 6. Compact Lie Groups; 6.1 Invariant Measures on Lie Groups; 6.2 Compact Linear Lie Groups; 6.3 Group Characters and Representations; Problems; Chapter 7. The Rotation Group and Its Representations; 7.1 The Groups SO(3) and SU(2); 7.2 Irreducible Representations of SU(2)
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7.3 Irreducible Representations of sl ( 2 )7.4 Expansion Theorems for Functions on SU(2); 7.5 New Realizations of the Irreducible Representations; 7.6 Applications to Physics; 7.7 The Clebsch-Gordan Coefficients; 7.8 Applications of the Clebsch-Gordan Series; 7.9 Double-Valued Representations of the Crystallographic Groups; 7.10 The Wigner-Eckart Theorem and Its Applications; 7.11 Spinor Fields and Invariant Equations; Problems; Chapter 8. The Lorentz Group and Its Representations; 8.1 The Homogeneous Lorentz Group; 8.2 The Physical Significance of Lorentz Invariance
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8.3 Representations of the Lorentz Group8.4 Models of the Representations; 8.5 Lorentz-Invariant Equations; Problems; Chapter 9. Representations of the Classical Groups; 9.1 Representations of the General Linear Groups; 9.2 Character Formulas; 9.3 The Irreducible Representations of GL(m, R), SL(m, E), and SU(m); 9.4 The Symplectic Groups and Their Representations; 9.5 The Orthogonal Groups and Their Representations; 9.6 Dirac Matrices and the Spin Representations of the Orthogonal Groups; 9.7 Examples and Applications; 9.8 The Pauli Exclusion Principle and the Periodic Table
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9.9 The Group Ring Revisited
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English
Weitere Ausg.:
ISBN 0-12-497460-0
Sprache:
Englisch
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