Momentum scale expansion of sharp cutoff flow equations

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~{\rm 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)

.

Note:

31 pages including 5 eps figures, uses harvmac and epsf

field theory: scalar
effective action
renormalization group
expansion: momentum
potential: local
invariance: reparametrization

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