  We study Feynman chekers - one of the most elementary models of electron
motion. It is also known as one-dimensional quantum walk or an Ising model at
imaginary temperature. We add the simpliest nontrivial electromagnetic field to
the model and find the limits of the resulting model for a small lattice step
and a large time, similar to the results by J. Narlikar 1972 and G. Grimmet -
S. Jason - P. Scudo from the 2000s. It turns out that the limits in the model
with the field are obtained from the known ones without a field by a mass
renormalization. We also find an exact solution for the resulting model.
