A Heisenberg algebra bundle of a vector field in three-space and its Weyl quantization

In these notes we associate a natural Heisenberg group bundle H-a with a singularity free smooth vector field X = (id,a) on a submanifold M in a Euclidean three-space. This bundle yields naturally an infinite dimensional Heisenberg group H-X(infinity). A representation of the C*-group algebra of H-X(infinity) is a quantization. It causes a natural Weyl-deformation quantization of X. The influence of the topological structure of M on this quantization is encoded in the Chem class of a canonical complex line bundle inside H-a.