  A spacetime-varying fine structure constant alpha(x^mu) could generate
quantum corrections in some of the coefficients of the Lorentz-violating
standard model extension (SME) associated with electrically charged fermions.
The quantum corrections depend on d_mu alpha, the spacetime gradient of the
fine structure constant. Lorentz-violating operators involving fermions arise
from the one-loop corrections to the quantum electrodynamics (QED) vertex
function and fermion self-energy. Both g^(lambda mu nu) and c^(mu nu) terms are
generated, at O(d_mu alpha) and O[(d_mu alpha)^2], respectively. The g^(lambda
mu nu) terms so generated are different in the vertex and self-energy, which
represents a radiatively induced violation of gauge invariance.
