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

TL;DR

This paper clarifies the relationship between wave function renormalization in Wilson actions and 1PI actions within the exact renormalization group framework, emphasizing the role of two independent cutoff functions.

Contribution

It establishes a detailed connection between wave function renormalizations of Wilson and 1PI actions using dual cutoff functions, extending previous work.

Findings

Clarified the relation between Wilson and 1PI wave function renormalizations.

Highlighted the importance of two independent cutoff functions.

Connected results to prior studies by Bervillier, Rosten, and Osborn & Twigg.

Abstract

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 & Twigg.