  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.
