  The field of a traveling circularly polarized electromagnetic wave and a
constant magnetic field localizes fermions perpendicularly to propagation of
the wave in the cross section of the order of the wavelength. Unusual exact
solutions of the Dirac equation correspond to this localization. Except to
routine use of thin fermion beams it can be suitable for alternative
measurements of the g - factor. Details and peculiarities of the solutions in
application to the measurements are considered in the paper.
