Dynamical q-deformation in quantum theory and the stochastic limit

We show that in a model of a particle interacting with a quantum field, the field operators rescaled according to the prescriptions of the stochastic limit, obey q-commutational relations with q depending on time. After the s tochastic limit, due to the nonlinearity, the particle and field degrees of freedom become entangled even at a kinematical level in the sense that the field and the atomic variables no longer commute but give rise to a new al gebra with new commutation relations replacing the boson ones. This allows to give a simple proof of the fact that the non-crossing half-planar diagra ms give the dominating contribution in a weak-coupling regime and to calcul ate explicitly the correlations associated with the new algebra.