  We study a method to obtain invariants under area-preserving diffeomorphisms
associated to closed curves in the plane from classical Yang-Mills theory in
two dimensions. Taking as starting point the Yang-Mills field coupled to non
dynamical particles carrying chromo-electric charge, and by means of a
perturbative scheme, we obtain the first two contributions to the on shell
action, which are area-invariants. A geometrical interpretation of these
invariants is given.
