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The Exact Renormalisation Group and Approximate Solutions

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arxiv hep-ph/9308265 v3 pith:QF2GKA66 submitted 1993-08-12 hep-ph hep-th

classification hep-phhep-th
keywords approximationcutoffaccurateactionapproximatebehaviourcactuscarefully
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abstract

We investigate the structure of Polchinski's formulation of the flow equations for the continuum Wilson effective action. Reinterpretations in terms of I.R. cutoff greens functions are given. A promising non-perturbative approximation scheme is derived by carefully taking the sharp cutoff limit and expanding in `irrelevancy' of operators. We illustrate with two simple models of four dimensional $\lambda \varphi^4$ theory: the cactus approximation, and a model incorporating the first irrelevant correction to the renormalized coupling. The qualitative and quantitative behaviour give confidence in a fuller use of this method for obtaining accurate results.

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