# Recursive Green's function approach to Feenberg perturbation theory

## TL;DR

This paper introduces a recursive Green's function method that refines perturbation series in quantum systems, aligning with Feenberg perturbation theory and removing repetitive terms for improved accuracy.

## Contribution

It presents a novel recursive Green's function approach that generalizes Brillouin-Wigner perturbation theory and effectively eliminates repetition terms in the series.

## Key findings

- Green's functions remove all repetition terms from perturbation series
- Diagonal elements of Green's functions yield effective propagators
- Method aligns with Feenberg perturbation theory

## Abstract

We propose a new procedure by using the recursive Green's functions which remove all the repetition terms from the time-independent perturbation series for finite-level quantum systems. These Green's functions are introduced as a generalization of the Brillouin-Wigner perturbation theory and the calculations of their diagonal elements can naturally give the effective propagators which are equal to the ones in the Feenberg perturbation theory.