  We develop a formalism for particle production in a field theory coupled to a
strong time-dependent external source. An example of such a theory is the Color
Glass Condensate. We derive a formula, in terms of cut vacuum-vacuum Feynman
graphs, for the probability of producing a given number of particles. This
formula is valid to all orders in the coupling constant. The distribution of
multiplicities is non--Poissonian, even in the classical approximation. We
investigate an alternative method of calculating the mean multiplicity. At
leading order, the average multiplicity can be expressed in terms of retarded
solutions of classical equations of motion. We demonstrate that the average
multiplicity at {\it next-to-leading order} can be formulated as an initial
value problem by solving equations of motion for small fluctuation fields with
retarded boundary conditions. The variance of the distribution can be
calculated in a similar fashion. Our formalism therefore provides a framework
to compute from first principles particle production in proton-nucleus and
nucleus-nucleus collisions beyond leading order in the coupling constant and to
all orders in the source density. We also provide a transparent interpretation
(in conventional field theory language) of the well known
Abramovsky-Gribov-Kancheli (AGK) cancellations. Explicit connections are made
between the framework for multi-particle production developed here and the
framework of Reggeon field theory.
