Dirac and Weyl Equations on a Lattice as Quantum Cellular Automata

Details Dirac and Weyl Equations on a Lattice as Quantum Cellular Automata Dirac and Weyl Equations on a Lattice as Quantum Cellular Automata

1993-04-19

arxiv.org/abs/hep-th/9304070v1

Phys.Rev. D49 (1994) 6920-6927

Physics

High Energy Physics

High Energy Physics - Theory

6, RevTeX

Scientific paper

10.1103/PhysRevD.49.6920

A discretized time evolution of the wave function for a Dirac particle on a cubic lattice is represented by a very simple quantum cellular automaton. In each evolution step the updated value of the wave function at a given site depends only on the values at the nearest sites, the evolution is unitary and preserves chiral symmetry. Moreover, it is shown that the relationship between Dirac particles and cellular automata operating on two component objects on a lattice is indeed very close. Every local and unitary automaton on a cubic lattice, under some natural assumptions, leads in the continuum limit to the Weyl equation. The sum over histories is evaluated and its connection with path integrals and theories of fermions on a lattice is outlined.

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