One-loop calculations in Lorentz-breaking theories and proper-time method

Abstract

Abstract 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 $F_{\mu\nu}$, for two of the most studied minimal Lorentz-violating extensions of QED, the one characterized by the axial vector $b^{\mu}$ and the one involving the second-rank constant tensor $c^{\mu\nu}$.