In his book Mickelsson notices that the infinite-dimensional Grassmannian
manifold of Segal and Wilson admits a Spin^c structure and after this he
naturally considers the problem of defining a Dirac operator on it. Mickelsson
gives a possible candidate for such an operator but unfortunately it proves out
to be badly diverging and he leaves it as an open problem to introduce proper
modifications to his original construction in order to obtain a well-defined
(unbounded) operator with expected properties.