Se p 20 03 ASSOCIATIVE ALGEBRAS , PUNCTURED DISKS AND THE QUANTIZATION OF POISSON MANIFOLDS

Abstract. The aim of this note is to provide an introduction to the algebraic, geometric and quantum field theoretic ideas that lie behind the KontsevichCattaneo-Felder formula for the quantization of Poisson structures, and to show how the quantization formula itself naturally arises when one couples the form a Feynman integral should have in order to reproduce the given Poisson structure as the first order term of its perturbative expansion, with the form it should have to describe an associative algebra. It is further shown how the Magri-Koszul brackets on 1-forms naturally fits into the theory of the Poisson sigma-model.