  We present a new completely elementary model that describes the creation,
annihilation, and motion of non-interacting electrons and positrons along a
line. It is a modification of the model known under the names Feynman checkers
or one-dimensional quantum walk. It can be viewed as a six-vertex model with
certain complex weights of the vertices. The discrete model is consistent with
the continuum quantum field theory, namely, reproduces the known expected
charge density as the lattice step tends to zero. It is exactly solvable in
terms of hypergeometric functions. We introduce interaction resembling Fermi's
theory and establish perturbation expansion.
