Space of signed points and the self-dual model

We study a generalization of the group of loops that is based on sets of signed points, instead of paths or loops. This geometrical setting incorporates the kinematical constraints of the sigma model, inasmuch as the group of loops does with Bianchi identities of Yang-Mills theories. We employ an Abelian version of this construction to quantize the self-dual model, which allows us to relate this theory with that of a massless scalar field obeying nontrivial boundary conditions.