Quantum Mechanics on Moduli Spaces

It has been assumed that it is possible to approximate the interactions of quantized BPS solitons by quantising a dynamical system induced on a moduli space of soliton parameters. General properties of the reduction of quantum systems by a Born-Oppenheimer approximation are described here and applied to sigma models and their moduli spaces in order to learn more about this approximation. New terms arise from the reduction proceedure, some of them geometrical and some of them dynamical in nature. The results are generalised to supersymmetric sigma models, where most of the extra terms vanish.