  For a general vector field we exhibit two Hilbert spaces, namely the space of
so called closed functions and the space of exact functions and we calculate
the codimension of the space of exact functions inside the larger space of
closed functions. In particular we provide a new approach for the known cases:
the Glauber field and the second-order Ginzburg-Landau field, and for the case
of the fourth-order Ginzburg-Landau field.
