On multivariable Zassenhaus formula

Abstract

We give a recursive algorithm to compute the multivariable Zassenhaus formula {\mathrm{e}}^{{{\displaystyle X}}_{\mathrm{1}}+{{\displaystyle X}}_{\mathrm{2}}+\mathrm{...}+{{\displaystyle X}}_n}={\mathrm{e}}^{{{\displaystyle X}}_{\mathrm{1}}}{\mathrm{e}}^{{{\displaystyle X}}_{\mathrm{2}}}\mathrm{...}{\mathrm{e}}^{{{\displaystyle X}}_n}{{\displaystyle \mathrm{\Pi }}}_{k=\mathrm{2}}^{\infty }{\hspace{0.17em}\mathrm{e}}^{{{\displaystyle W}}_k} and derive ane effective recursion formula of {{\displaystyle W}}_k.

Keywords

Baker-Campbell-Hausdor_ formula / Zassenhaus formula

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Higher Education Press and Springer-Verlag GmbH Germany, part of Springer Nature