Non-exponential decay for Polaron model

A model of a particle interacting with a quantum field is considered. The m odel includes as particular cases the polaron model and non-relativistic qu antum electrodynamics. We compute matrix elements of the evolution operator in the stochastic approximation and show that, depending on the state of t he particle, one can get non-exponential decay with the rate t(-3/2) In the process of computation a new algebra of commutation relations that can be considered as an operator deformation of the quantum Boltzmann commutation relations is used. (C) 1999 Published by Elsevier Science B.V. All rights r eserved.