Combinatorial Approach to Boson Anti-Normal Ordering Problem

TL;DR

This paper presents a combinatorial method using Stirling numbers and Bell polynomials to solve the anti-normal ordering problem for quantum operators, extending existing operational techniques.

Contribution

It introduces a systematic combinatorial framework for anti-normal ordering, utilizing Stirling numbers and Bell polynomials, building on recent theoretical advancements.

Findings

Derived explicit formulas for anti-normal ordering using combinatorial methods

Extended operational techniques with Stirling numbers and Bell polynomials

Validated the approach with specific operator examples

Abstract

We address a systematic combinatorial approach to the anti-normal ordering problem. In this way, we use the Stirling numbers and their generating function, the so-called Bell polynomials, together with the operational methods to anti-normal the operator ${e^{\lambda {a^\dag}a}}$. In fact, we exploit the new theorem given by Sh\"ahandeh et al. in a special case of anti-normal ordering.