  Asymptotic single-particle states in quantum field theories with small
departures from Lorentz symmetry are investigated perturbatively with focus on
potential phenomenological ramifications. To this end, one-loop radiative
corrections for a sample Lorentz-violating Lagrangian contained in the
Standard-Model Extension (SME) are studied at linear order in Lorentz
breakdown. It is found that the spinor kinetic operator, and thus the
free-particle physics, is modified by Lorentz-violating operators absent from
the original Lagrangian. As a consequence of this result, both the standard
renormalization procedure as well as the Lehmann-Symanzik-Zimmermann reduction
formalism need to be adapted. The necessary adaptations are worked out
explicitly at first order in Lorentz-breaking coefficients.
