THE STRATONOVICH-WEYL CORRESPONDENCE FOR ONE-DIMENSIONAL KINEMATICAL GROUPS

The Stratonovich-Weyl correspondence is a restatement of the Moyal quantization where the phase space is a manifold and where a group of transformations acts on it transitively. The first and most important step is to define a mapping from the manifold into the set of self-adjoint operators on a Hilbert space, under suitable conditions. This mapping is called a Stratonovich-Weyl kernel. The construction of this mapping is discussed on coadjoint orbits of the one-dimensional Galilei, Poincare, and Newton-Hooke groups as well as the two-dimensional Euclidean group.