Chern-Simons Soliton Dynamics in Modular Parameter Space

We study dynamics of non-relativistic Chern-Simons solitons, both in the absence and in the presence of external fields. We find that a phase, related to the $1$-cocyle of the Galileo group, must be included to give the correct dynamical behavior. We show that interactions among Chern-Simons solitons are mediated by an effective Chern-Simons gauge field induced by the solitons. In the two soliton case, we evaluate analytically the effective interaction Lagrangian, which previously was found numerically.