A Comment on the Relationship Between Differential and Dimensional Renormalization

TL;DR

This paper reveals a simple relationship between differential and dimensional renormalization methods in quantum field theory, highlighting the advantages of the differential approach for low-order Feynman graphs.

Contribution

It demonstrates that differential renormalization can produce the same results as dimensional renormalization without altering spacetime dimensions.

Findings

Differential and dimensional renormalization are closely related for low-order graphs.

Differential renormalization avoids changing spacetime dimensions.

Both methods yield equivalent finite results in massless quantum field theories.

Abstract

We show that there is a very simple relationship between differential and dimensional renormalization of low-order Feynman graphs in renormalizable massless quantum field theories. The beauty of the differential approach is that it achieves the same finite results as dimensional renormalization without the need to modify the space time dimension.