# Higher order derivative operators as quantum corrections

## TL;DR

This paper introduces a ghost-free coupling between gauge and fermionic fields, deriving quantum corrections including higher derivative terms and the Lee-Wick term in the photon effective action, with calculations of the one-loop effective action and electron self-energy.

## Contribution

It presents a novel non-minimal, ghost-free coupling model that yields higher order derivative quantum corrections and the Lee-Wick term in the photon effective action.

## Key findings

- Derivation of the one-loop photon effective action including Euler-Heisenberg and Lee-Wick terms.
- Identification of quantum corrections leading to higher derivative operators.
- Calculation of the leading order electron self-energy.

## 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.