Hamiltonian derivation of the point vortex model from the two-dimensional nonlinear Schrödinger equation

We present a rigorous derivation of the point vortex model starting from the two-dimensional nonlinear Schr{ö}dinger equation, from the Hamiltonian perspective, in the limit of well-separated, subsonic vortices on the background of a spatially-infinite strong condensate. As a corollary, we calculate to high accuracy the self-energy of an isolated elementary Pitaevskii vortex, for the first time.