  We discuss applications of the proper-time method in various minimal Lorentz
violating modifications of QED and present new results obtained with its use.
Explicitly. we calculate the complete one-loop Heisenberg-Euler effective
action involving all orders in $F_{mn}$, for two of the most studied minimal
Lorentz-violating extensions of QED, the one characterized by the axial vector
$b^m$ and the one involving the second-rank constant tensor $c^{mn}$.
