Non-exponential decay for Polaron model

A model of a particle interacting with a quantum field is considered. The model includes as particular cases the polaron model and non-relativistic quantum electrodynamics. We compute matrix elements of the evolution operator in the stochastic approximation and show that, depending on the state of the 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 reserved.