  This series of papers models the dynamics of a large set of interacting
neurons within the framework of statistical field theory. The system is
described using a two-field model. The first field represents the neuronal
activity, while the second field accounts for the interconnections between
cells. This model is derived by translating a probabilistic model involving a
large number of interacting cells into a field formalism. The current paper
focuses on deriving the background fields of the system, which describe the
potential equilibria in terms of interconnected groups. Dynamically, we explore
the perturbation of these background fields, leading to processes such as
activation, association, and reactivation of groups of cells.
