Bundles over Moduli Spaces and the Quantization of BPS Monopoles

A vector bundle over the moduli space of BPS monopoles is constructed from the zero-modes of the Dirac operator acting on iso-spinor spinors and coupled to BPS monopoles. This bundle of zero-modes is an index bundle and has a natural connection whose curvature is anti-self-dual. For monopoles of charge one or two this information is sufficient for a detailed description of the bundle structure and the connection. Physically, the bundle of zero-modes is interpreted as a model for the quantum dynamics of monopoles coupled to one fermion: the quantum mechanical wavefunction is a section of the bundle and the quantum Hamiltonian is the Laplace-Beltrami operator on the moduli space minimally coupled to the natural connection. Numerical calculations of hound state energies and scattering cross sections are presented and the qualitative implications of the bundle geometry for the quantum theory are emphasised.