Closed constraint algebras and path integrals for loop group actions

In this paper we study systems with a closed algebra of second class constr aints. We describe a construction of the reduced theory that resembles the conventional treatment of first class constraints. It suggests, in particul ar, 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 applie d 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 o btain a 2-form from a fiber (path) integral. This form is not closed as a r elict of the anomaly. Examples of such reduced spaces are provided by D-bra nes on group manifolds with WZW action. (C) 2001 American Institute of Phys ics.