Determining equations for higher-order decompositions of exponential operators

TL;DR

This paper reviews the theory of exponential operator decompositions and introduces a scheme using Lyndon words to derive explicit formulas for decomposition coefficients.

Contribution

It presents a novel scheme employing Lyndon words to systematically derive determining equations and explicit formulas for higher-order exponential operator decompositions.

Findings

Explicit formulas for decomposition coefficients are derived.

A systematic scheme for constructing determining equations is proposed.

The approach enhances the accuracy of exponential operator decompositions.

Abstract

The general decomposition theory of exponential operators is briefly reviewed. A general scheme to construct independent determining equations for the relevant decomposition parameters is proposed using Lyndon words. Explicit formulas of the coefficients are derived.