  In this note we study systems with a closed algebra of second class
constraints. We describe a construction of the reduced theory that resembles
the conventional treatment of first class constraints. It suggests, in
particular, to compute the symplectic form on the reduced space by a fiber
integral of the symplectic form on the original space. This approach is then
applied to a class of systems with loop group symmetry. The chiral anomaly of
the loop group action spoils the first class character of the constraints but
not their closure. Proceeding along the general lines described above, we
obtain a 2-form from a fiber (path)integral. This form is not closed as a
relict of the anomaly. Examples of such reduced spaces are provided by D-branes
on group manifolds with WZW action.
