  We analyze the helicity conservation following from the axial Ward identity
for the massless fermion. We discuss the pair production of a fermion, $\ell$,
and an anti-fermion, $\bar{\ell}$, from the annihilation process of photons,
$\gamma$'s and conclude that the chirality production is prohibited in any
annihilation process of on-shell $\gamma$'s. We demonstrate this selection rule
in the tree-level process of $\gamma+\gamma\to \ell+\bar{\ell}$. We next
consider the off-shell effect on the chirality production in the presence of
the background magnetic field. We point out that the particle conversion
process under the magnetic field induces the polarization of an incident
$\gamma$, which can also be interpreted intuitively from the helicity
conservation.
