Pair creation in electric fields, anomalies, and renormalization of the electric current

TL;DR

This paper studies pair creation in strong electric fields, addressing renormalization ambiguities using anomalies, and extends regularization methods to ensure consistent electric current calculations in quantum electrodynamics.

Contribution

It introduces a resolution to the adiabatic order ambiguity in renormalization by using anomalies and extends regularization techniques to different dimensions and particle spins.

Findings

Renormalization ambiguity can be fixed via conformal anomaly.

Extended adiabatic regularization to spinor QED in two dimensions.

Demonstrated renormalization of electric current in Sauter pulse.

Abstract

We investigate the Schwinger pair production phenomena in spatially homogeneous strong electric fields. We first consider scalar QED in four-dimensions and discuss the potential ambiguity in the adiabatic order assignment for the electromagnetic potential required to fix the renormalization subtractions. We argue that this ambiguity can be solved by invoking the conformal anomaly when both electric and gravitational backgrounds are present. We also extend the adiabatic regularization method for spinor QED in two-dimensions and find consistency with the chiral anomaly. We focus on the issue of the renormalization of the electric current $\langle j^\mu \rangle$ generated by the created pairs. We illustrate how to implement the renormalization of the electric current for the Sauter pulse.