On the q-analogues of the Zassenhaus formula for dientangling exponential operators

Abstract

Katriel, Rasetti and Solomon introduced a $q$-analogue of the Zassenhaus formula written as $e_q^{(A+B)}$ $=$ $e_q^A{e}_q^B{e}_q^{c_2}{e}_q^{c_3}{e}_q^{c_4}{e}_q^{c_5}...$, where $A$ and $B$ are two generally noncommuting operators and $e_q^z$ is the Jackson $q$-exponential, and derived the expressions for $c_2$, $c_3$ and $c_4$. It is shown that one can also write $e_q^{(A+B)}$ $=$ $e_q^Ae_q^Be_{q^2}^{\C_2}e_{q^3}^{\C_3}e_{q^4}^{\C_4}e_{q^5}^{\C_5}...$. Explicit expressions for $\C_2$, $\C_3$ and $\C_4$ are given.

12 Pages. New references have been added. Title and Abstract have been modified in view of an earlier work of Katriel, Rasetti and Solomon on a different form of the q-Zassenhaus formula. The text is modified only slightly since the result of the paper is unchanged

Cited by in corpus (1)

• Closed forms of the Zassenhaus formula