We consider the Poisson sigma model associated to a Poisson manifold. The
perturbative quantization of this model yields the Kontsevich star product
formula. We study here the classical model in the Hamiltonian formalism. The
phase space is the space of leaves of a Hamiltonian foliation and has a natural
groupoid structure. If it is a manifold then it is a symplectic groupoid for
the given Poisson manifold. We study various families of examples. In
particular, a global symplectic groupoid for a general class of two-dimensional
Poisson domains is constructed.Comment: 34 page
