  We investigate the precisely measured anomalous magnetic moment and Lamb
shift as tests for the possible existence of the radiatively induced Lorentz
and CPT violation effects in quantum electrodynamics. To this end we calculate
the one-loop vacuum polarization tensor and vertex radiative correction in
dimensional reduction and on-shell renormalization scheme. We explicitly show
how the Lorentz and CPT violation sector affects the anomalous magnetic moment
and Lamb shift. Remarkably, we find infrared divergences coming from Lorentz
and CPT violating term that do not cancel in physical cross sections. This
result appears to place stringent constraints on the type of Lorentz/CPT
violating terms that can be added to the QED Lagrangian.
