Zeta functions, renormalization group equations, and the effective action

TL;DR

This paper presents a method to derive one-loop renormalization group equations and leading-logarithm corrections to the effective action in quantum field theories using Seeley--DeWitt coefficients.

Contribution

It introduces a systematic way to extract renormalization group equations and improve the effective action for arbitrary quantum field theories at one loop.

Findings

Derived all one-loop RG equations from Seeley--DeWitt coefficients

Renormalization group improved the classical action

Calculated leading-logarithm corrections to the one-loop effective action

Abstract

We demonstrate how to extract all the one-loop renormalization group equations for arbitrary quantum field theories from knowledge of an appropriate Seeley--DeWitt coefficient. By formally solving the renormalization group equations to one loop, we renormalization group improve the classical action, and use this to derive the leading-logarithms in the one-loop effective action for arbitrary quantum field theories.