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

Authors:
R. Sridhar;R. Jagannathan
Affiliations:
The Institute of Mathematical Sciences, C.I.T. Campus, Tharamani, Chennai, TN 600113, India;The Institute of Mathematical Sciences, C.I.T. Campus, Tharamani, Chennai, TN 600113, India
Venue:
Journal of Computational and Applied Mathematics - Special issue: Proceedings of the international conference on special functions and their applications
Year:
2003

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Abstract

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.