Momentum Scale Expansion of Sharp Cutoff Flow Equations

Abstract

We show how the exact renormalization group for the effective action with a sharp momentum cutoff, may be organised by expanding one-particle irreducible parts in terms of homogeneous functions of momenta of integer degree (Taylor expansions not being possible). A systematic series of approximations -- the $O(p^M)$ approximations -- result from discarding from these parts, all terms of higher than the $M^{\mathrm{th}}$ degree. These approximations preserve a field reparametrization invariance, ensuring that the field's anomalous dimension is unambiguously determined. The lowest order approximation coincides with the local potential approximation to the Wegner-Houghton equations. We discuss the practical difficulties with extending the approximation beyond $O(p^0)$.

Comments: 31 pages including 5 eps figures, uses harvmac and epsf. Minor additions -- not worth the bandwidth if you already have a copy