  We generalise the study of constraints imposed by supersymmetry on the Berry
connection to transformations with component fields in representations of an
internal symmetry group G. Since the fields act as co-ordinates of the
underlying space one finds a non-trivial extension to its structure and,
correspondingly, there are new non-abelian constraints on the Berry connection.
The specific case of G=SU(2) is shown to constrain the connection to behave as
a magnetic monopole over su(2), its Lie algebra.
