Summing the derivative expansion of the effective action

TL;DR

This paper presents a method to exactly sum the first and second derivatives in the derivative expansion of the effective action, improving the perturbative approach for large derivatives.

Contribution

It introduces a technique to sum the leading derivatives exactly and handle higher derivatives perturbatively in the effective action expansion.

Findings

Exact summation of first and second derivatives achieved.

Perturbative treatment of higher derivatives demonstrated.

Enhanced accuracy in effective action calculations for large derivatives.

Abstract

The derivative expansion of the effective action is a perturbative development in derivatives of the fields. The expansion breaks down when some of the derivatives are too large. We show how to sum exactly the first and second derivatives and treat perturbatively derivatives higher than second.