HOPF TERM AND THE EFFECTIVE LAGRANGIAN FOR THE SKYRMIONS IN A 2-DIMENSIONAL ELECTRON-GAS AT SMALL G-FACTOR

We study interacting electrons in two dimensions moving in the lowest Landau level under the condition that the Zeeman energy is much smalle r than the Coulomb energy and the filling factor is one. In this case, Skyrmion quasiparticles play an important role. Here, we present a si mple and transparent derivation of the corresponding effective Lagrang ian. In its kinetic part, we find a nonzero Hopf term, the prefactor o f which we determine rigorously. In the Hamiltonian part, we calculate , by means of a gradient expansion, the Skyrmion-Skyrmion interaction completely up to fourth order in spatial derivatives.