Fermionic quantum field theories as probabilistic cellular automata

A class of fermionic quantum field theories with interactions is shown to be equivalent probabilistic cellular automata, namely automata a probability distribution for the initial states. Probabilistic on one-dimensional lattice are two-dimensional fermions. They can viewed as generalized Ising models square and therefore classical statistical systems. As they Thus mechanics emerges from statistics. an explicit example interacting theory we describe type discretized Thirring model automaton. The updating rule automaton encoded in step evolution operator that expressed terms annihilation creation operators. complex structure associated particle-hole transformations. naive continuum limit exhibits Lorentz symmetry. We exploit equivalence order show how concepts wave functions, density matrix, noncommuting operators observables similarity transformations convenient useful description automata.