The study of formal deformation quantization implies a deformation of the formal parameter. The purpose of this lecture is to give some concrete examples of deformation quantization of Fréchet-Poisson algebras and to show how certain unusual phenomena appear. On the other hand, although having achieved an important degree of development, its convergence problem seems not clear at the moment. We propose a convergence approach for deformation quantization by setting up the Fréchet category. The most interesting phenomena will appear in relation to the associativity of the *-product, which will reveal a new aspect of geometry.
Deformation quantization of Fréchet-Poisson algebras
Updated 14/09/2005