A new approach to the Baker-Campbell-Hausdorff expansion

TL;DR

This paper introduces a novel diagrammatic series expansion for the logarithm of the product of exponentials of noncommutative variables, providing a new method to handle Baker-Campbell-Hausdorff expansions.

Contribution

It presents a new diagram-based approach to express the Baker-Campbell-Hausdorff expansion for noncommutative variables, with terms as infinite sums in powers of x-y.

Findings

Series represented by diagrams simplifies calculations.

Provides explicit formulas for each term in the expansion.

Enhances understanding of noncommutative exponential products.

Abstract

For noncommutative variables x,y an expansion of log(exp(x)exp(y)) in powers of x+y is obtained.Each term of the series is given by an infinite sum in powers of x-y.The series is represented by diagrams.