  In the present paper, we consider in detail the aspects of the Heisenberg's
equations of motion, related to their transformation to the representation
dependent of external sources. We provide with a closed solution as to the
variation-derivative motion equations in the general case of a normal form
(symbol) chosen. We show that the action in the path integral does depend
actually on a particular choice of a normal symbol. We have determined both the
aspects of the latter dependence: the specific boundary conditions for virtual
trajectories, and the specific boundary terms in the action.
