Free probability and quantum electrodynamics

Abstract

The stochastic limit of a flee particle coupled to the quantum electromagnetic field without dipole approximation leads to many new features such as: interacting Fock space, Hilbert module commutation relations, disappearance of the crossing diagrams, etc. In the present paper we begin to study how the situation is modified if a free particle is replaced by a particle in a potential which is the Fourier transform of a bounded measure.We prove that the stochastic limit procedure converges and that the overall picture is similar to the free case with the important difference that the structure of the limit Hilbert module is strongly dependent on the wave operator of the particle.