  We introduce a lattice model for a static and isotropic system of
relativistic fermions. An action principle is formulated, which describes a
particle-particle interaction of all fermions. The model is designed
specifically for a numerical analysis of the nonlinear interaction, which is
expected to lead to the formation of a Dirac sea structure. We discuss basic
properties of the system. It is proved that the minimum of the variational
principle is attained. First numerical results reveal an effect of spontaneous
symmetry breaking.
