Phase-Integral Formulation of Dynamically Assisted Schwinger Pair Production

TL;DR

This paper develops a phase-integral approach to analyze how combined strong and weak electromagnetic fields enhance scalar particle pair production, providing explicit formulas and a systematic power series expansion in the Keldysh parameter.

Contribution

It introduces a systematic phase-integral formulation for dynamically assisted Schwinger pair production, including explicit formulas and a numerical evaluation procedure.

Findings

Derived a power series expansion of the WKB action in the Keldysh parameter.

Provided explicit formulas for a superimposed constant and oscillating field.

Proposed a numerical method for evaluating pair production density.

Abstract

We present a phase-integral formulation of dynamically assisted Schwinger pair production of scalar charges to find the pair production density under a strong low-frequency field and a weak high-frequency field. The leading WKB action was the Schwinger formula determined by the constant field, whose corrections are determined by the Keldysh parameter for the oscillating field, $m\omega_{q}/qE_{q}$. We found a systematic expression of the leading WKB action as a power series in the Keldysh parameter, of which coefficients are given as integrals of the product of fields in the complex time domain. For the case of a strong constant field superimposed with a weak oscillating field, we provided explicit formulas and proposed a procedure for numerical evaluation. The presented phase-integral formulation should provide a clear simple method for quantitatively analyzing the leading-order features of dynamically assisted Schwinger pair production.