The full Lorentz-violating vacuum polarization tensor: Low- and high-energy limits

Abstract

In this paper, we compute the full vacuum polarization tensor in the fermion sector of Lorentz-violating quantum electrodynamics (QED). It turns out to be that even if we assume momentum routing invariance of the Feynman diagrams, it is not possible to fix all surface terms and find an ambiguity-free vacuum polarization tensor. The high- and low-energy limits of this tensor are obtained explicitly. In the high-energy limit, only [Formula: see text] coefficients contribute to the result. In the low-energy limit, we find that Lorentz-violating-induced terms depend on [Formula: see text], [Formula: see text] and [Formula: see text] coefficients and vanish at [Formula: see text]. At small [Formula: see text], we succeeded to obtain implications for condensed matter systems, explicitly, for the Hall effect in Weyl semi-metals.