# Explicit Description of the Zassenhaus Formula

## TL;DR

This paper provides an explicit infinite series expansion of the Zassenhaus formula for the exponential of a sum of operators, offering a new perspective on the Baker-Campbell-Hausdorff formula.

## Contribution

It introduces a novel explicit description of the Zassenhaus formula and offers an alternative expression for the Baker-Campbell-Hausdorff formula.

## Key findings

- Explicit infinite sum expansion of e^{A+B}
- New expression for the Baker-Campbell-Hausdorff formula
- Enhanced understanding of operator exponential decompositions

## Abstract

We explicitly describe an expansion of $e^{A+B}$ as an infinite sum of the products of $B$ multiplied by the exponential function of $A$. This is the explicit description of the Zassenhaus formula. We also express the Baker-Campbell-Hausdorff formula in a different manner.