The Auxiliary Mass Method beyond the Local Potential Approximation

TL;DR

This paper extends the auxiliary mass method by deriving a next-to-leading approximation of the evolution equation, connecting it to a series from the effective action's derivative expansion, thus advancing theoretical understanding.

Contribution

It introduces a next-to-leading approximation for the evolution equation in the auxiliary mass method, linking it to a derivative expansion series.

Findings

Derived an expression for the next-to-leading approximation.

Connected the evolution equation to a series from the effective action.

Provided a partial differential equation for improved approximation.

Abstract

We show that the evolution equation of the effective potential in the auxiliary mass method corresponds to a leading approximation of a certain series. This series is derived from an evolution equation of an effective action using a derivative expansion. We derived an expression of the next-to-leading approximation of the evolution equation, which is a simultaneous partial differential equation.