  In the generic domain wall fermion formulation of chiral fermions on the
lattice, the zero modes of the four-dimensional Wilson fermion operator with
the negative mass parameter $-M_5$ introduce unphysical massive modes
propagating in the four-dimensional spacetime. In the free fermion case, the
pole mass of this kind of unphysical modes is given by $\tilde{E}=\ln(1-M_5)$,
which acquires an imaginary part, $i\pi$, when $M_5>1$ and results in an
oscillatory behavior of the domain wall fermion propagator in time. The
existence of the unphysical modes in the presence of gauge fields is
investigated in the mean field approximation, and their physical consequences
are discussed. In addition, we also give a semiquantitative criterion for
tuning $M_5$ in the realistic numerical study.
