A demonstration of scheme independence in scalar ERGs

TL;DR

This paper demonstrates that in scalar exact renormalization group equations, physical quantities like the one-loop beta function remain scheme-independent despite different kernel choices, emphasizing universality in RG analysis.

Contribution

It shows that the one-loop beta function in scalar ERGs can be expressed solely in terms of effective action vertices, ensuring scheme independence.

Findings

One-loop beta function is scheme-independent.

Universal results are recovered regardless of kernel choice.

Effective action vertices determine physical quantities.

Abstract

The standard demand for the quantum partition function to be invariant under the renormalization group transformation results in a general class of exact renormalization group equations, different in the form of the kernel. Physical quantities should not be sensitive to the particular choice of the kernel. Such scheme independence is elegantly illustrated in the scalar case by showing that, even with a general kernel, the one-loop beta function may be expressed only in terms of the effective action vertices, and in this way the universal result is recovered.