  In this paper we intend to complement the identification given in Kuerten &
Fernandes-Silva [1] (Mod. Phys. Lett. A. Vol. 33, No. 16) which relates the
axion to a metric spinor phase by means of Maxwell's theory in the Infeld-van
der Waerden's {\gamma}-formalism. Thus, we obtain two alternative
identifications: the first focuses on Dirac's theory so that when obtaining an
axion-like phase-fermion coupling, we achieve the first identification, and the
last one investigates the phase behavior under Peccei-Quinn rotations in order
to show that the phase changes as an axion pseudoparticle. With the formal
aspects established, we also study the semiclassical fermion-photon system to
demonstrate that the magnetic monopole current defined in [1] has dyon charge
in flat universe and acquires a Witten effect form when there is a demand for
chiral symmetry.
