In the present paper, the basic ideas of the stochastic limit of quant
um theory are applied to quantum electro-dynamics. This naturally lead
s to the study of a new type of quantum stochastic calculus on a Hilbe
rt module. Our main result is that in the weak coupling limit of a sys
tem composed of a free particle (electron, atom,...) interacting, via
the minimal coupling, with the quantum electromagnetic field, a new ty
pe of quantum noise arises, living on a Hilbert module rather than a H
ilbert space. Moreover we prove that the vacuum distribution of the li
miting field operator is not Gaussian, as usual, but a nonlinear defor
mation of the Wigner semi-circle law. A third new object arising from
the present theory, is the so-called interacting Fock space. A kind of
Fock space in which the n quanta, in the n-particle space, are not in
dependent, but interact. The origin of all these new features is that
we do not introduce the dipole approximation, but we keep the exponent
ial response term, coupling the electron to the quantum electromagneti
c field. This produces a nonlinear interaction among all the modes of
the limit master field (quantum noise) whose explicit expression, that
we find, can be considered as a nonlinear generalization of the Fermi
golden yule.