The Ginzburg-Landau Equation II. The Energy Of Vortex Configurations

We consider the Ginzburg-Landau equation in dimension two. We introduce a key notion of the energy of vortex configurations. It is defined by minimizing the renormalized Ginzburg-Landau (free) energy introduced in the previous paper over functions with a given set of zeros of given local indices. This notion allows us to define the vortex interaction and vortex Hamiltonian in a canonical way. We find asymptotic behaviour of this energy as the intervortex distances grow. To this end we use several novel techniques