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In the current paper the properties of a quantum field theory based oncertain sets of Lorentz-violating coefficients in the nonminimal fermion sectorof the Standard-Model Extension are analyzed. In particular, three families ofcoefficients are considered, where two of them are CPT-even and the third isCPT-odd. As a first step the modified fermion dispersion relations areobtained. Then the positive- and negative-energy solutions of the modifiedDirac equation and the fermion propagator are derived. These are used todemonstrate the validity of the optical theorem at tree-level, which provides across-check for the results obtained. Furthermore unitarity is examined andseems to be valid for the first set of CPT-even coefficients. However for theremaining sets certain issues with unitarity are found. The articledemonstrates that the adapted quantum field theoretical methods at tree-levelwork for the nonminimal, Lorentz-violating framework considered. Besides, thequantum field theory based on the first family of CPT-even coefficients is mostlikely well-behaved at lowest order perturbation theory. The results areimportant for future phenomenological investigations carried out in the contextof field theory, e.g., the computation of decay rates and cross sections attree-level.

Quantum field theoretic properties of Lorentz-violating operators of nonrenormalizable dimension in the fermion sector