Benchmarking regulator-sourced 2PI and average 1PI flow equations in zero dimensions

TL;DR

This paper compares two approaches, regulator-sourced 2PI and average 1PI, for deriving exact flow equations in a zero-dimensional quantum field theory, highlighting their differences and consistency.

Contribution

It provides a detailed benchmarking of the regulator-sourced 2PI and average 1PI flow equations in a simplified zero-dimensional setting, revealing their structural differences.

Findings

Both approaches are self-consistent.

Key differences in their behavior and loop expansion structure.

Clarification of the simple parametric dependence in zero dimensions.

Abstract

We elucidate the regulator-sourced 2PI and average 1PI approaches for deriving exact flow equations in the case of a zero dimensional quantum field theory, wherein the scale dependence of the usual renormalisation group evolution is replaced by a simple parametric dependence. We show that both approaches are self-consistent, while highlighting key differences in their behaviour and the structure of the would-be loop expansion.