Radiatively induced Lorentz and $CPT$ violation in electrodynamics

In a nonperturbative formulation, radiative corrections arising from Lorentz and CPT violation in the fermion sector induce a definite and nonzero Chern-Simons addition to the electromagnetic action. If instead a perturbative formulation is used, an infinite class of theories characterized by the value of the Chern-Simons coefficient emerges at the quantum level. {copyright} {ital 1999} {ital The American Physical Society}