  Distinctive features in the sub-dynamics of an interacting bipartite system
are explored. The sub-dynamic Heisenberg operators are introduced in a novel
way leading to the quasi-particle-like concept in the respective subsystems.
This formulation is illustrated using the known exact solutions of the generic
(Jaynes - Cummings) model of interacting bipartite system of a spin 1/2
particle and a single mode electromagnetic field (more generally, boson field).
The striking effects of interaction and entanglement are reflected in the
dressing of the non-interacting number and spin representations, displaying
quasi-particle-like properties. This development may be at the heart of the
physics of back - action discussed in the recent literature.
