  Two types of particles, A and B with their corresponding antiparticles, are
defined in a one dimensional cyclic lattice with an odd number of sites. In
each step of time evolution, each particle acts as a source for the
polarization field of the other type of particle with nonlocal action but with
an effect decreasing with the distance: A -->...\bar{B} B \bar{B} B \bar{B} ...
; B --> A \bar{A} A \bar{A} A ... . It is shown that the combined distribution
of these particles obeys the time evolution of a free particle as given by
quantum mechanics.
