  We present a Fermionic Cellular Automaton model which describes massless
Dirac fermion in 1+1 dimension coupled with local, number preserving
interaction. The diagonalization of the two particle sector shows that specific
values of the total momentum and of the coupling constant allows for the
formation of bound states. Furthermore, we present a classification of the
local number-preserving interactions that are invariant under the isotropy
group of the cellular automaton which simulates the Weyl equation.
