Equivalence of Wilson Actions

TL;DR

This paper introduces the concept of equivalence among Wilson actions, derives the exact renormalization group transformation for scalar theories, and demonstrates universality of critical exponents, simplifying Wilson's formalism using Polchinski's approach.

Contribution

It defines equivalence of Wilson actions and connects Wilson's and Polchinski's formalisms, providing a clearer understanding of renormalization group transformations and universality.

Findings

Derived the exact RG transformation for scalar theories

Proved universality of critical exponents at fixed points

Simplified Wilson's formalism using Polchinski's approach

Abstract

We introduce the concept of equivalence among Wilson actions. Applying the concept to a real scalar theory on a euclidean space, we derive the exact renormalization group transformation of K. G. Wilson, and give a simple proof of universality of the critical exponents at any fixed point of the exact renormalization group transformation. We also show how to reduce the original formalism of Wilson to the simplified formalism by J. Polchinski.