  In Lorentz violating quantum electrodynamics (QED) it is known that a
radiatively induced Chern-Simons term appears in the effective action for the
gauge field, which is finite but undetermined. This ambiguity is shown to be
absent in a condensed matter realization of such a theory in Weyl semi-metals
due to the existence of a full microscopic model from which this effective
theory emerges. Physically observable consequences such as birefringence are
also discussed in this scenario.
