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

Publishing date

2002-12-24

URL

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

Science

Physics

Field

Mathematical Physics

Additional info

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

Type

Scientific paper

Abstract

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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