The Exact Renormalisation Group and Approximate Solutions

Details The Exact Renormalisation Group and Approximate Solutions The Exact Renormalisation Group and Approximate Solutions

1993-08-12

arxiv.org/abs/hep-ph/9308265v3

Int.J.Mod.Phys. A9 (1994) 2411-2450

Physics

High Energy Physics

High Energy Physics - Phenomenology

49 pages (with figures), Plain TeX, uses psfig, 7 postscript figures appended as uuencoded compressed tar file, SHEP 92/93-27,

Scientific paper

10.1142/S0217751X94000972

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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