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Chern-Simons terms in Lifshitz like quantum electrodynamics

In this work the generation of generalized Chern-Simons terms in three dimensional quantum electrodynamics with high spatial derivatives is studied. We analyze the self-energy corrections to the gauge field propagator by considering an expansion of the amplitude up to third order in the external momenta. The divergences of the corrections are determined and explicit forms for the Chern-Simons terms with high derivatives are obtained. Some unusual aspects of the calculation are stressed and the existence of a smooth isotropic limit is proved. The transversality of the anisotropic gauge propagator is also discussed.