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 modification of the mass sector through the addition of the term proportional to the antisymmetric tensor Hμν. 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 Fμν. Our result is shown to be UV finite, and it is confirmed using the Feynman diagrams framework.