Closed forms of the Zassenhaus formula

Abstract The Zassenhaus formula finds many applications in theoretical physics or mathematics, from fluid dynamics to differential geometry. non-commutativity of the elements algebra implies that exponential a sum operators cannot be expressed as product exponentials operators. can then decomposed multiplied by supplementary term which takes generally form an infinite exponentials. Such procedure is often referred ‘disentanglement’. However, for some special commutators, closed forms found. In this work, we propose when commutator X ˆ and $\hat{Y}$?> Y satisfy relation $[\hat{X},\hat{Y}] = u\hat{X}+v\hat{Y}+c\unicode{x1D7D9}$?> stretchy="false">[ , stretchy="false">] = u + v c