The Exact Renormalization Group and Approximate Solutions
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 Green’s functions are given. A promising nonperturbative approximation scheme is derived by carefully taking the sharp cutoff limit and expanding in “irrelevancy” of operators. We illustrate with two simple models of fourdimensional λφ^{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.
 Publication:

International Journal of Modern Physics A
 Pub Date:
 1994
 DOI:
 10.1142/S0217751X94000972
 arXiv:
 arXiv:hepph/9308265
 Bibcode:
 1994IJMPA...9.2411M
 Keywords:

 High Energy Physics  Phenomenology;
 High Energy Physics  Theory
 EPrint:
 49 pages (with figures), Plain TeX, uses psfig, 7 postscript figures appended as uuencoded compressed tar file, SHEP 92/9327, CERNTH.6977/93, Note Added with more complete comparison to earlier work