GEOMETRIC AND MATAPLECTIC QUANTIZATION

Abstract. Geometric quantization gives a representation of the algebra of classical observ-ables of a dynamical system, described through a symplectic manifold, in the Lie algebra of operators acting on a Hilbert space. We review and compare the geometrical and topological key ingredients of two approaches to this type of quantization, the original Kostant-Souriau-Kirillov prequantization procedure and the more recent metaplectic quantization introduced by K. Habermann, which uses some properties of the symplectic Dirac operator. The com-parison shows that, besides the difference between the two constructions, they fit into the same framework and give rise to standard features of the quantization problem. 1