  Fock modules for multi-dimensional Virasoro algebras (non-central extensions
of the diffeomorphism algebra vect(N)) have recently been reported. Using ideas
from the antifield formalism, I construct new classes of lowest-energy modules,
as cohomology groups of a certain Fock complex. The Fock construction involves
a passage to p-jets prior to normal ordering, but the abelian charges usually
diverge in the limit p --> oo. The requirement of a finite limit imposes severe
restrictions on the number of spacetime dimensions and on the order of the
Euler-Lagrange (EL) equations. Under some natural assuptions (the EL equations
are first order for fermions and second order for bosons, and no reducible
gauge symmetries appear), finiteness is only possible when the number of
spacetime dimensions N = 4.
