WEYL, DIRAC, AND MAXWELL EQUATIONS ON A LATTICE AS UNITARY CELLULAR-AUTOMATA

Very simple unitary cellular automata on a cubic lattice are introduce d to model a discretized time evolution of the wave functions for spin ning particles. In each evolution step the updated value of the wave f unction at a given site depends only on the values at the nearest site s. The discretized evolution is also unitary and preserves chiral symm etry. The case of the spin-1/2 particle is studied in detail, and it i s shown that every local and unitary automaton on a cubic lattice, und er some natural assumptions, leads in the continuum limit to the Weyl equation. The sum over histories is evaluated and is shown to reproduc e the retarded propagator in the continuum limit. Generalizations to i nclude massive particles (Dirac theory), spin-1 particles (Maxwell the ory), and higher-spin particles are also described.