We present a fermionic cellular automaton model which describes massless Dirac fermions 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 allow 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.
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Centofanti et al. (2024) studied this question.
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