We discuss applications of the proper-time method in a Lorentz-violating extension of QED characterized by the modification of the mass sector through the addition of the term proportional to the antisymmetric tensor H⏛⏜. Unlike other LV extensions of QED, in our case the one-loop Euler-Heisenberg-like action turns out to include only odd degrees of the stress tensor F⏛⏜. Our result is shown to be UV finite, and it is confirmed using the Feynman diagrams framework.
Araújo et al. (Sun,) studied this question.