  Higher-order effects of CPT and Lorentz violation within the SME effective
framework including Myers-Pospelov dimension-five operator terms are studied.
The model is canonically quantized by giving special attention to the arising
of indefinite-metric states or ghosts in an indefinite Fock space. As is
well-known, without a perturbative treatment that avoids the propagation of
ghost modes or any other approximation, one has to face the question of whether
unitarity and microcausality are preserved. In this work, we study both
possible issues. We found that microcausality is preserved due to the
cancellation of residues occurring in pairs or conjugate pairs when they become
complex. Also, by using the Lee-Wick prescription, we prove that the $S$ matrix
can be defined as perturbatively unitary for tree-level $2\to 2$ processes with
an internal fermion line.
