Harmonic Analysis on Homogeneous Spaces: Second Edition (Dover Books on Mathematics) | A Mathematical Companion to Quantum Mechanics (Dover Books on Physics) | Quantum Theory, Groups and Representations: An Introduction | Gravitation | Differential Geometry, Lie Groups, and Symmetric Spaces | Symmetry, Representations, and Invariants | Quantum Field Theory
The first chapters cover certain geometric preliminaries, advancing to discussions of symplectic geometry and the application of its concepts to the action of a Lie group on a symplectic manifold. Subsequent chapters address Fourier analysis, the metaplectic representation, and quantization. A final chapter on the Kirillov theory applies the ideas of the previous chapters to homogeneous symplectic manifolds of nilpotent Lie groups. The book concludes with an Appendix on Quantum Mechanics by Robert Hermann.
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