Zassenhaus formula exponents

Question

found Zassenhaus formula for noncommutative $X,Y$ $$e^{t(X+Y)}= e^{tX}~ e^{tY} ~e^{-\frac{t^2}{2} [X,Y]} ~ e^{\frac{t^3}{6}(2[Y,[X,Y]]+ [X,[X,Y]] )} ~ e^{\frac{-t^4}{24}([[[X,Y],X],X] + 3[[[X,Y],X],Y] + 3[[[X,Y],Y],Y]) } \cdots$$ Please, how could I getexponents of higher order in Zassenhaus formula?

Answer 1

Check the reference F. Casas, A. Murua, M. Nadinic, "Efficient computation of the Zassenhaus formula", Computer Physics Communications 183 (2012), 2386-2391. It contains even a mathematica code for generating all the terms in the formula