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

We clarify the relation between the wave function renormalization for Wilson actions and that for the 1PI actions in the exact renormalization group formalism. Our study depends crucially on the use of two independent cutoff functions for the Wilson actions. We relate our results to those obtained previously by Bervillier, Rosten, and Osborn u0026 Twigg.