One-loop Euler-Heisenberg action in Lorentz-violating QED revisited

We discuss applications of the proper-time method in a Lorentz-violating extension of QED characterized by the addition of the term proportional to the antisymmetric tensor $H_{\mu\nu}$. Unlike other LV extensions of QED, in our case, the one-loop Euler-Heisenberg-like action turns out to include only odd powers of the stress tensor $F_{\mu\nu}$. Our result is shown to be UV finite, and it is confirmed using the Feynman diagrams framework.