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

摘要

Katriel, Rasetti and Solomon introduced a q-analogue of the Zassenhaus formula written as eq(A+B)=eqAeqBeqc2eqc3eqc4eqc5…, where A and B are two generally noncommuting operators and eqz is the Jackson q-exponential, and derived the expressions for c2, c3 and c4. It is shown that one can also write eq(A+B)=eqAeqBeq2C2eq3C3eq4C4eq5C5…. Explicit expressions for C2, C3 and C4 are given.