A note on the Zassenhaus product formula

Daniel Scholz; Michael Weyrauch

doi:10.1063/1.2178586

paper

A note on the Zassenhaus product formula

arXiv:math-ph/0603016 · doi:10.1063/1.2178586

Abstract

We provide a simple method for the calculation of the terms c_n in the Zassenhaus product $e^{a + b} = e^{a} e^{b} \prod_{n = 2}^{\infty} e^{c_{n}}$ for non-commuting a and b. This method has been implemented in a computer program. Furthermore, we formulate a conjecture on how to translate these results into nested commutators. This conjecture was checked up to order n=17 using a computer.