  We project the Wilson/Polchinski renormalization group equation onto its
uniform external field dependent effective free energy and connected Green's
functions. The result is a hierarchy of equations which admits a choice of
"natural" truncation and closure schemes for nonperturbative approximate
solution. In this way approximation schemes can be generated which avoid power
series expansions in either fields or momenta. When following one closure
scheme the lowest order equation is the mean field approximation, while another
closure scheme gives the "local potential approximation." Extension of these
closure schemes to higher orders leads to interesting new questions regarding
truncation schemes and the convergence of nonperturbative approximations. One
scheme, based on a novel "momentum cluster decomposition" of the connected
Green's functions, seems to offer new possibilities for accurate
nonperturbative successive approximation.
