  We define and study the Cauchy problem for a 1-D nonlinear Dirac equation
with nonlinearities concentrated at one point. Global well-posedness is
provided and conservation laws for mass and energy are shown. Several examples,
including nonlinear Gesztesy-\v{S}eba models and the concentrated versions of
the Bragg Resonance, Gross-Neveu, and Soler type models, all within the scope
of the present paper, are given. The key point of the proof consists in the
reduction of the original equation to a nonlinear integral equation for an
auxiliary, space-independent variable (the "charge").
