ISBN: B0006BNTTC
Title: Lie groups for physicists (The Mathematical physics monograph series)
Author: Robert Hermann
Publisher: W. A. Benjamin
Publication Date: 1966
Number Of Pages: 193
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Chapter 3. LIE ALGEBRAS AND THE CORRESPONDENCE BETWEEN SUBGROUPS AND SUBALGEBRAS 8
Chapter 4. SEMISIMPLE LIE ALGEBRAS 14
Chapter 5. COMPACT AND NONCOMPACT SEMISIMPLE LIE ALGEBRAS 19
Dual Symmetric Spaces 19
Complete Reducibility of Representations of Semisimple Groups 26
Complex Semisimple Lie Algebras 28
Chapter 6. CONJUGACY OF CARTAN SUBALGEBRAS AND DECOMPOSITIONS OF SEMISIMPLE LIE GROUPS 30
Chapter 7. THE IWASAWA DECOMPOSITION 40
Chapter 8. FINITE-DIMENSIONAL REPRESENTATION OF COMPACT LIE ALGEBRAS 45
Chapter 9. VECTOR BUNDLES AND INDUCED REPRESENTATIONS 52
Multiplier and Unitary Representations 60
Vector Bundles on Projective Space 65
Representations of SLB, R) 68
Chapter 10. REPRESENTATIONS. UNIVERSAL ENVELOPING ALGEBRA AND INVARIANT DIFFERENTIAL EQUATIONS 72
Representations and Differential Equations 76
The Dirac Equation 79
Chapter 11. LIMITS AND CONTRACTIONS OF LIE GROUPS 86
Contraction of the Lorentz Group to the Gallilean Group 88
Contraction and Asymptotic Behavior of Special Functions 91
Limits of Induced Representations 93
Limits of Noncompact Symmetric Subgroups 94
Limits within Semidirect Products 97
Extensions and Possible Further Physical Applications of the Limit Idea 98
The Relation between Contraction and Limit of Lie Algebras 98
Chapter 12. DECOMPOSITION OF TENSOR PRODUCTS OF INDUCED REPRESENTATIONS 102
Chapter 13. THE GROUP-THEORETIC VERSION OF THE FOURIER TRANSFORM 109
Chapter 14. COMPACTIFICATIONS OF HOMOGENEOUS SPACES 117
Grassmanian Compactifications of Homogeneous Spaces 118
Chapter 15. ON THE CLASSIFICATION OF SUBGROUPS 124
Maximal Subalgebras of Maximal Rank of Compact Lie Algebras 125
Maximal Complex Subalgebras of Maximal Rank of the Complex Simple Lie Algebras 130
Chapter 16. GROUP-THEORETIC PROBLEMS IN PARTICLE QUANTUM MECHANICS 132
Harmonic Oscillators 141
The Hydrogen Atom 144
Strong-Coupling Theory for the Hydrogen Atom 149
Chapter 17. GROUPS IN ELEMENTARY-PARTICLE PHYSICS 150
Perturbation Theory and Groups 157
Gauge Groups and Supermultiplet Theory 160
Chapter 18. FURTHER TOPICS IN THE THEORY OF REPRESENTATIONS OF NONCOMPACT SEMISIMPLE GROUPS 163
Reproducing Kernels for Representations 171
Line-Bundle Representations on Symmetric Spaces 172
Representations Obtained from Noncompact Groups
Acting on Compact Symmetric Spaces 179
Gell-Mann's Formula 182
References 185
Index 189
发表于 2007-1-14 01:33:45