  In this paper, we show that the Hamiltonian approach to loop quantum gravity
has a fermion doubling problem. To obtain this result, we couple loop quantum
gravity to a free massless scalar and a chiral fermion field, gauge fixing the
many fingered time gauge invariance by interpreting the scalar field as a
physical clock. We expand around a quantum gravity state based on a regular
lattice and consider the limit where the bare cosmological constant is large
but the fermonic excitations have energies low in Planck units. We then make
the case for identifying the energy spectrum in this approximation with that of
a model of lattice fermion theory which is known to double.
