A Lattice Model for the Fermionic Projector in a Static and Isotropic Space-Time

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.