  In this series of three papers, we generalize the derivation of dual photons
and monopoles by Polyakov, and Banks, Myerson and Kogut, to obtain
approximative models of SU(2) lattice gauge theory. The papers take three
different representations as their starting points: the representation as a BF
Yang-Mills theory, the spin foam representation and the plaquette
representation. The derivations are based on stationary phase approximations.
  In this first article, we cast 3- and 4-dimensional SU(2) lattice gauge
theory in the form of a lattice BF Yang-Mills theory. In several steps, the
expectation value of a Wilson loop is transformed into a path integral over a
dual gluon field and monopole-like degrees of freedom. The action contains the
tree-level Coulomb interaction and a nonlinear coupling between dual gluons,
monopoles and current.
