Operator perturbation theory in the backward Heisenberg picture

TL;DR

This paper introduces a simplified operator perturbation theory in the backward Heisenberg picture, which uses backward time evolution to streamline the perturbation expansion process, avoiding the Dyson series.

Contribution

The paper proposes a novel backward Heisenberg picture that simplifies perturbation expansions and relates to Kubo's density operator approach.

Findings

Perturbation expansion is simplified in the backward Heisenberg picture.

The approach avoids the Dyson expansion.

Relationship with Kubo's density operator is discussed.

Abstract

We present a simple operator perturbation theory in the backward Heisenberg picture. Compared with the well-known Heisenberg picture, the revised picture is based on the backward time instead of the forward time. The unique feature of the uncommon picture is that the perturbation expansion becomes very simple and the famous Dyson expansion is not directly involved. Its relationship with the perturbation expansion for the density operator developed by Kubo is also discussed.