MOMENTUM SCALE EXPANSION OF SHARP CUTOFF FLOW EQUATIONS

We show how the exact renormalization group for the effective action w ith a sharp momentum cutoff, may be organized by expanding one-particl e irreducible parts in terms of homogeneous functions of momenta of in teger degree (Taylor expansions not being possible). A systematic seri es of approximations - the O(p(M)) approximations - result from discar ding from these parts, all terms of higher than the M(th) degree. Thes e approximations preserve a field reparametrization invariance, ensuri ng that the field's anomalous dimension is unambiguously determined. T he lowest order approximation coincides with the local potential appro ximation to the Wegner-Houghton equations. We discuss the practical di fficulties with extending the approximation beyond O(p(0)).