Group Theory and Its Applications

List of ContributorsPrefaceContents of Other VolumesFinite Groups and Semisimple Algebras in Quantum Mechanics I. Introduction II. Linear Associative Algebras III. Semisimple Algebras IV. Semisimple Algebras in Quantum Mechanics V. Group Algebras VI. Fundamental Representation Theory VII. Sequence Adaptation VIII. Induced and Subduced Representations IX. Approximate Symmetries in Quantum Mechanics X. Weakly Interacting Sites XI. Double Sequence Adaptation and Recoupling Coefficients XII. Recoupling Coefficients in Quantum Mechanics XIII. Point Group Symmetry Adaptation XIV. Branching Rules XV. Double Cosets XVI. Effective Hamiltonians for Weakly Interacting Sites XVII. Conclusion ReferencesSemisimple Subalgebras of Semisimple Lie Algebras: The Algebra ??5(SU(6)) as a Physically Significant Example I. Introduction II. Definitions III. Embedding of Subalgebras IV. Regular Subalgebras V. S-Subalgebras VI. Classification of Subalgebras of the Algebra ??5 VII. Inclusion Relations VIII. Physically Significant Chains of Subalgebras of ??5 ReferencesFrobenius Algebras and the Symmetric Group I. Introduction II. The Frobenius Algebra and Its Centrum III. The Matric Basis and Symmetry Adaptation IV. The Algebra of the Symmetric Group V. Isospin-Free Nuclear Theory VI. Spin-Free (Supermultiplet) Nuclear Theory VII. Spin-Free Atomic Theory VIII. Summary ReferencesThe Heisenberg-Weyl Ring in Quantum Mechanics I. Introduction II. The Heisenberg-Weyl Group III. The Heisenberg-Weyl Ring ?? IV. The Quantization Process V. Canonical Transformations VI. Quantum Mechanics on a Compact Space ReferencesComplex Extensions of Canonical Transformations and Quantum Mechanics I. Introduction and Summary II. Groups of Classical Canonical Transformations III. Unitary Representations of Canonical Transformations in Quantum Mechanics IV. Complex Phase Space and Bargmann Hilbert Space V. Complex Extensions of Canonical Transformations VI. Barut Hilbert Space and Angular Momentum Projection in Bargmann Hilbert Space VII. Applications to Problems of Accidental Degeneracy in Quantum Mechanics VIII. The Three-Body Problem IX. Applications to the Clustering Theory of Nuclei X. Conclusion ReferencesQuantization as an Eigenvalue Problem I. Quantization II. Operators on Hilbert Space III. Differential Equation Theory IV. Symplectic Boundary Form V. Spectral Density VI. Continuation in the Complex Eigenvalue Plane VII. One-Dimensional Relativistic Harmonic Oscillator VIII. Survey ReferencesElementary Particle Reactions and the Lorentz and Galilei Groups I. Introduction II. Single-Variable Expansions for Four-Body Scattering III. Lorentz Group Two-Variable Expansions for Spinless Particles and the Lorentz Amplitudes IV. Two-Variable Expansions Based on the O(4) Group for Three-Body Decays V. O(3,1) and O(4) Expansions for Particles with Arbitrary Spins VI. Explicitly Crossing Symmetric Expansions Based on the O(2,1) Group VII. Two-Variable Expansions of Nonrelativistic Scattering Amplitudes Based on the E(3) Group VIII. Two-Variable Expansions Based on the Group SU(3) and Their Generalizations IX. Conclusions ReferencesAuthor IndexSubject Index