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

Consequences of a condensed matter realization of Lorentz violating QED in Weyl semi-metals