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

TL;DR

This paper calculates the full vacuum polarization tensor in Lorentz-violating QED, analyzing its behavior at different energy scales and implications for condensed matter phenomena like the Hall effect in Weyl semimetals.

Contribution

It provides the complete form of the Lorentz-violating vacuum polarization tensor and explores its high and low energy limits, highlighting the dependence on specific Lorentz-violating coefficients.

Findings

High energy limit involves only c_{μν} coefficients.

Low energy limit depends on b_{μ}, c_{μν}, g_{μνλ} coefficients.

Lorentz-violating terms are suppressed by p^2/m^2.

Abstract

We compute the full vacuum polarization tensor in the fermion sector of Lorentz-violating QED. Even if we assume momentum routing invariance of the Feynman diagrams, it is not possible to fix all surface terms and find an unambiguity free vacuum polarization tensor. The high and low energy limits of this tensor is presented. In the high energy limit, only $c_{\mu\nu}$ coeffcients contribute. In the low energy limit, we fnd that Lorentz-violating induced terms depend only on $b_{\mu}$, $c_{\mu\nu}$ and $g_{\mu\nu\lambda}$ coeffcients and they are suppressed by powers of $\frac{p^{2}}{m^{2}}$. This limit allows to obtain implications for condensed matter systems, explicitly, for the Hall effect in Weyl semimetals.