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We study the fermionic sector of the Myers and Pospelov theory with a generalbackground $n$. The spacelike case without temporal component is well definedand no new ingredients came about, apart from the explicit Lorentz invarianceviolation. The lightlike case is ill defined and physically discarded. However,the other case where a nonvanishing temporal component of the background ispresent, the theory is physically consistent. We show that new modes appear asa consequence of higher time derivatives. We quantize the timelike theory andcalculate the microcausality violation which turns out to occur near the lightcone.

Microcausality and quantization of the fermionic Myers-Pospelov model