  In their study of the representation theory of loop groups, Pressley and
Segal introduced a determinant line bundle over an infinite dimensional
Grassmann manifold. Mickelsson and Rajeev subsequently generalized the work of
Pressley and Segal and in the process introduced for any p >=1 another infinite
dimensional Grassmann manifold and a determinant line bundle defined over it.
The construction of this determinant line bundle required the notion of a
regularized determinant for bounded operators. In this note we specialize to
the case p =2 and construct explicitly a connection on the corresponding
determinant line bundle and give a simple and explicit formula for its
curvature. As an application of our results we give a geometric derivation of
the Mickelsson-Rajeev cocycle.
