The Derivative Expansion of the Effective Action and the Renormalization Group Equation

TL;DR

This paper applies the renormalization group equation to the derivative expansion of the effective action, specifically analyzing the second derivative term in massless scalar models, and relates different renormalization schemes.

Contribution

It extends the renormalization group analysis to the second derivative term of the effective action in massless scalar theories, connecting on-shell and minimal subtraction schemes.

Findings

Expressed the kinetic term in terms of renormalization group functions.

Related renormalization group functions across different schemes.

Analyzed the derivative expansion in massless scalar models.

Abstract

The perturbative evaluation of the effective action can be expanded in powers of derivatives of the external field. We apply the renormalization group equation to the term in the effective action that is second order in the derivatives of the external field and all orders in a constant external field, considering both massless scalar $\phi_4^4$ model and massless scalar electrodynamics. A so-called ``on shell'' renormalization scheme permits one to express this ``kinetic term'' for the scalar field entirely in terms of the renormalization group functions appropriate for this scheme. These renormalization group functions can be related to those associated with minimal subtraction.