Completely equivariant ?

It would be very natural to consider trivial all infinitesimal deformations of Lagrangian submanifolds generated by the Hamiltonians of the form for any .

If we were able to construct some version of the form equivariant under all such trivial Hamiltonians, then we could have interpreted it as a form on the moduli space of BRST-exact deformations of the action. (Because a Hamiltonian of the form actually does not change the action at all.)

However, we have only been able to equivariantize for a subset of belonging to a subspace of satisfying some very restrictive conditions.

This is somewhat strange.