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We clarify the relation between the wave function renormalization for Wilsonactions and that for the 1PI actions in the exact renormalization groupformalism. Our study depends crucially on the use of two independent cutofffunctions for the Wilson actions. We relate our results to those obtainedpreviously by Bervillier, Rosten, and Osborn & Twigg.

On the wave function renormalization for Wilson actions and their 1PI actions