Exact scheme independence at one loop

TL;DR

This paper demonstrates that in four-dimensional scalar field theory, the one-loop beta function remains scheme-independent despite the variety of possible renormalization group kernels, emphasizing the universality of physical results.

Contribution

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

Findings

One-loop beta function is scheme-independent.

Effective action vertices determine the beta function.

Universal results are recovered regardless of kernel choice.

Abstract

The requirement that the quantum partition function be invariant under a renormalization group transformation results in a wide class of exact renormalization group equations, differing in the form of the kernel. Physical quantities should not be sensitive to the particular choice of the kernel. We demonstrate this scheme independence in four dimensional scalar field theory 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 thus, under very general conditions, the universal result is recovered.