We revisit the problem of quark production in high energy heavy ion collisions, at leading order in $alpha_s$ in the color glass condensate framework. In this first paper, we setup the formalism and express the quark spectrum in terms of a set of mod
e functions of the Dirac equation. We determine analytically their initial value in the Fock-Schwinger gauge on a proper time surface $Q_stau_0ll 1$, in a basis which makes manifest the boost invariance properties of this problem. We also describe a statistical algorithm to perform the sampling of the mode functions.
In this paper, we show how classical statistical field theory techniques can be used to efficiently perform the numerical evaluation of the non-perturbative Schwinger mechanism of particle production by quantum tunneling. In some approximation, we al
so consider the back-reaction of the produced particles on the external field, as well as the self-interactions of the produced particles.
The charged particle multiplicity in central AA collisions and the production of heavy flavors in pA collisions at the LHC is predicted in the CGC framework.
