Perturbative Expansion around the Gaussian Effective Action: The Background Field Method

TL;DR

This paper introduces a systematic perturbative expansion technique around the Gaussian effective action using the background field method, significantly improving approximation accuracy in quantum mechanical problems.

Contribution

It presents a novel systematic approach for perturbative expansion around the Gaussian effective action utilizing the background field method.

Findings

First non-trivial correction improves Gaussian approximation

Method applied successfully to quantum anharmonic oscillator

Enhances accuracy of Gaussian-based quantum approximations

Abstract

We develop a systematic method of the perturbative expansion around the Gaussian effective action based on the background field method. We show, by applying the method to the quantum mechanical anharmonic oscillator problem, that even the first non-trivial correction terms greatly improve the Gaussian approximation.