Operator perturbation theory in the backward Heisenberg picture
  We present a simple operator perturbation theory in the backward Heisenberg picture. Compared with the well-known Heisenberg picture, the revised picture is based on the backward time instead of the forward time. The unique feature of the uncommon picture is that the perturbation expansion becomes very simple and the famous Dyson expansion is not directly involved. Its relationship with the perturbation expansion for the density operator developed by Kubo is also discussed. 
Fei Liu and Ding-yang Liu
quant-ph cond-mat.stat-mech