Quark production in heavy ion collisions I. Formalism and boost invariant fermionic light-cone mode functions

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 mode 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.