CONTENTS I. Introduction............................................................................................................................................... 5 II. Preliminary notions................................................................................................................................ 7 III. Geometric quantization.........................................................................................................................12 A. Elements of symplectic geometry................................................................12 B. Quantum bundles...........................................................................................13 C. Polarizations....................................................................................................16 D. Hilbert space connected with a polarized symplectic manifold............ 18 E. Kostant quantization of physical quantities............................................... 28 IV. Kernel quantization............................................................................................................................... 41 A. Geometric quantization of canonical diffeomorphisms.......................... 41 B. Distinguished kernels................................................................................... 43 C. Kernel representation of quantized operators.......................................... 67 References.................................................................................................................................................. 78
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