  We study perturbative unitarity in a Lorentz-symmetry-violating QED model
with higher-order derivative operators in the light of the results of Lee and
Wick to preserve unitarity in indefinite metric theories. Specifically, we
consider the fermionic sector of the Myers-Pospelov model, which includes
dimension-five operators, coupled to standard photons. We canonically quantize
the model, paying attention to its effective character, and show that its
Hamiltonian is stable, emphasizing the exact stage at which the indefinite
metric appears and decomposes into a positive-metric sector and a
negative-metric sector. Finally, we verify the optical theorem at the one-loop
level in the annihilation channel of the forward-scattering process $e^+(p_2,
r) + e^-(p_1,s)$ by applying the Lee-Wick prescription in which the states
associated with the negative metric are left out from the asymptotic Hilbert
space, but nevertheless are considered in the loop integration via the
propagator.
