SPINORS AND SCALARS ON RIEMANN SURFACES

We study (magnetic) Dirac and Schrodinger operators for general two-di mensional manifolds. We find relations between them, and use these as tools for calculating ground-state degeneracies of various electronic systems (with and without spin). We find examples which have a degener ate ground state, although there are no symmetry operators commuting w ith the Schrodinger operator. The connection between the two operators is related to a Berry phase.