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Higher-order effects of CPT and Lorentz violation within the SME effectiveframework including Myers-Pospelov dimension-five operator terms are studied.The model is canonically quantized by giving special attention to the arisingof indefinite-metric states or ghosts in an indefinite Fock space. As iswell-known, without a perturbative treatment that avoids the propagation ofghost modes or any other approximation, one has to face the question of whetherunitarity and microcausality are preserved. In this work, we study bothpossible issues. We found that microcausality is preserved due to thecancellation of residues occurring in pairs or conjugate pairs when they becomecomplex. Also, by using the Lee-Wick prescription, we prove that the $S$ matrixcan be defined as perturbatively unitary for tree-level $2\to 2$ processes withan internal fermion line.

Tree-level unitarity, causality and higher-order Lorentz and CPT violation