Post-Wick theorems for symbolic manipulation of second-quantized expressions in atomic many-body perturbation theory

TL;DR

This paper introduces a set of theorems to simplify complex second-quantized expressions in atomic many-body perturbation theory, facilitating symbolic computation and diagram counting.

Contribution

It develops new theorems tailored for symbolic algebra tools to efficiently manipulate and simplify high-order perturbation expressions in many-body theory.

Findings

Derived rules enable efficient expression simplification.

Counted Brueckner-Goldstone diagrams in multiple perturbation orders.

Demonstrated practical application in diagram enumeration.

Abstract

Manipulating expressions in many-body perturbation theory becomes unwieldily with increasing order of the perturbation theory. Here I derive a set of theorems for efficient simplification of such expressions. The derived rules are specifically designed for implementing with symbolic algebra tools. As an illustration, we count the numbers of Brueckner-Goldstone diagrams in the first several orders of many-body perturbation theory for matrix elements between two states of a mono-valent system.