  The Standard-Model Extension (SME) parameterizes all possible
Lorentz-violating contributions to the Standard Model and General Relativity.
It can be considered as an effective framework to describe possible
quantum-gravity effects for energies much below the Planck energy. In the
current paper, the spin-nondegenerate operators of the SME fermion sector are
the focus. The propagators, energies, and solutions to the modified Dirac
equation are obtained for several families of coefficients including nonminimal
ones. The particle energies and spinors are computed at first order in Lorentz
violation and, with the optical theorem, they are shown to be consistent with
the propagators. The optical theorem is then also used to derive the matrices
formed from a spinor and its Dirac conjugate at all orders in Lorentz
violation. The results are the first explicit ones derived for the
spin-nondegenerate operators. They will prove helpful for future
phenomenological calculations in the SME that rely on the footing of quantum
field theory.
