The Wilson-Polchinski exact renormalization group equation

Details The Wilson-Polchinski exact renormalization group equation The Wilson-Polchinski exact renormalization group equation

2004-05-04

arxiv.org/abs/hep-th/0405025v2

Phys.Lett. A332 (2004) 93-100

Physics

High Energy Physics

High Energy Physics - Theory

Some minor changes, a reference added, typos corrected

Scientific paper

10.1016/j.physleta.2004.09.037

The critical exponent $\eta $ is not well accounted for in the Polchinski exact formulation of the renormalization group (RG). With a particular emphasis laid on the introduction of the critical exponent $\eta $, I re-establish (after Golner, hep-th/9801124) the explicit relation between the early Wilson exact RG equation, constructed with the incomplete integration as cutoff procedure, and the formulation with an arbitrary cutoff function proposed later on by Polchinski. I (re)-do the analysis of the Wilson-Polchinski equation expanded up to the next to leading order of the derivative expansion. I finally specify a criterion for choosing the ``best'' value of $\eta $ to this order. This paper will help in using more systematically the exact RG equation in various studies.

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