  We analyse the normalisable zero-modes of the Dirac operator on the Taub-NUT
manifold coupled to an abelian gauge field with self-dual curvature, and
interpret them in terms of the zero modes of the Dirac operator on the 2-sphere
coupled to a Dirac monopole. We show that the space of zero modes decomposes
into a direct sum of irreducible SU(2) representations of all dimensions up to
a bound determined by the spinor charge with respect to the abelian gauge
group. Our decomposition provides an interpretation of an index formula due to
Pope and provides a possible model for spin in recently proposed geometric
models of matter.
