Weyl Manifold: A Quantized Symplectic Manifold

Abstract

We give a brief review on Weyl manifold as a quantization of symplectic manifold, equipped with a system of quantized canonical charts and quantized canonical transformations among them called Weyl diffeomorphism. Weyl manifold is deeply related to deformation quantization on symplectic manifolds. We explain a relation between Weyl manifolds and deformation quantization.