A useful formula for evaluating commutators
Gregg M. Gallatin · Journal of Mathematical Physics · 1983
We present the derivation of a useful formula for evaluating commutators of the form [A, f (B)] and [ f (A),B], where the nested commutators [A,[A,[⋅⋅⋅[A[A,B]]⋅⋅⋅]]] and [[[⋅⋅⋅[[A,B],B]⋅⋅⋅],B],B] do not vanish in general. The use of this formula is illustrated by a simple example.