Quark propagation in the random instanton vacuum

This is the first of a series of papers devoted to a systematic study of QCD correlation functions. Our aim is to reach a quantitative understanding of the forces between quarks in all channels, and, in particular, the role played by instanton-induced effects. The topic of this first paper is to work out approximate formulae for quark propagators in a multi-instanton environment, which include the 't Hooft interaction to all orders. As an application, we use the simplest possible model of the kind, the so-called "random instanton liquid model" (RILM). The results obtained can also be related to properties of heavy-light mesons, and those are found to be consistent with phenomenology.