  We study radiative corrections to massless quantum electrodynamics modified
by two dimension-five LV interactions $\bar{\Psi} \gamma^{\mu} b'^{\nu}
F_{\mu\nu}\Psi$ and $\bar{\Psi}\gamma^{\mu}b^{\nu} \tilde{F}_{\mu\nu} \Psi$ in
the framework of effective field theories. All divergent
one-particle-irreducible Feynman diagrams are calculated at one-loop order and
several related issues are discussed. It is found that massless quantum
electrodynamics modified by the interaction $\bar{\Psi} \gamma^{\mu} b'^{\nu}
F_{\mu\nu}\Psi$ alone is one-loop renormalizable and the result can be
understood on the grounds of symmetry. In this context the one-loop
Lorentz-violating beta function is derived and the corresponding running
coefficients are obtained.
