  In loop quantum gravity the discrete nature of quantum geometry acts as a
natural regulator for matter theories. Studies of quantum field theory in
quantum space-times in spherical symmetry in the canonical approach have shown
that the main effect of the quantum geometry is to discretize the equations of
matter fields. This raises the possibility that in the case of fermion fields
one could confront the usual fermion doubling problem that arises in lattice
gauge theories. We suggest, again based on recent results on spherical
symmetry, that since the background space-times will generically involve
superpositions of states associated with different discretizations the
phenomenon may not arise. This opens a possibility of incorporating chiral
fermions in the framework of loop quantum gravity.
