Time dependent Baker-Hausdorf formula

[paweld]

Could anyone show me the Baker-Hausdorf formula for product of exponentials in case of
operators which are time dependent. I know that there is a time-dependent version of this
formula which works under some assumptions are imposed on the operators which appear
in exponentials, like e.g. commutator commutes with all operators.
Thanks.

 

[Bill_K]

Forgive me, but I don't see why any time-dependence would matter. It's an identity which applies to any and all operators. (I assume you're talking about the full theorem that includes double commutators, triple commutators, etc, not one that has been truncated.)

 

[paweld]

Thanks for answer. I looked for the identity which involves time ordered exponentials
and includes only double commutators. Fortunantely I've just found paper
(http://www.sciencedirect.com/science/article/pii/S0167691101001943)
where a formula which enabled me to compute what I wanted was given.