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

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

2002-12-24

arxiv.org/abs/math-ph/0212068v2

Physics

Mathematical Physics

12 Pages. New references have been added. Title and Abstract have been modified in view of an earlier work of Katriel, Rasetti

Scientific paper

Katriel, Rasetti and Solomon introduced a $q$-analogue of the Zassenhaus formula written as $e_q^{(A+B)}$ $=$ $e_q^Ae_q^Be_q^{c_2}e_q^{c_3}e_q^{c_4}e_q^{c_5}...$, 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.

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