Higher order derivative operators as quantum corrections

Abstract: In this paper we propose a non-minimal, and ghost free, coupling between the gauge field and the fermionic one from which we obtain, perturbatively, terms with higher order derivatives as quantum corrections to the photon effective action in the low energy regime. We calculate the one-loop effective action of the photon field and show that, in addition to the Euler-Heisenberg terms, the well known Lee-Wick term, $\sim F_{\mu\nu}\partial_{\alpha}\partial^{\alpha}F^{\mu\nu}$, arises in low energy regime as a quantum correction from the model. We also obtain the electron self energy in leading order.