Abstract
The widely used locally constant field approximation (LCFA) can be utilized in order to derive a simple closed-form expression for the total number of particles produced in the presence of a strong electromagnetic field of a general spatiotemporal configuration. A usual justification for this approximate approach is the requirement that the external field vary slowly in space and time. In this investigation, we examine the validity of the LCFA by comparing its predictions to the results obtained by means of exact nonperturbative numerical techniques. To benchmark the LCFA in the regime of small field amplitudes and low frequencies, we employ a semiclassical approach. As a reference, we consider a standing electromagnetic wave oscillating both in time and space as well as two spatially uniform field configurations: Sauter pulse and oscillating electric field. Performing a thorough numerical analysis, we identify the domain of the field parameters where the approximation is well justified. In particular, it is demonstrated that the Keldysh parameter itself is not a relevant quantity governing the accuracy of the LCFA. It is also found that for field amplitudes close to the Schwinger critical value, the LCFA may overestimate the particle yield. We discuss how this effect is related to the Pauli exclusion principle and quantum interference.
Highlights
The widely used locally constant field approximation (LCFA) can be utilized in order to derive a simple closed-form expression for the total number of particles produced in the presence of a strong electromagnetic field of a general spatiotemporal configuration
One of the most remarkable phenomena predicted by quantum electrodynamics (QED) is the process of electronpositron pair production in strong external fields [1,2,3,4]
We will benchmark the LCFA against the exact results obtained with the aid of the quantum kinetic equations (QKE) and Furrypicture formalism for two different scenarios involving spatially homogeneous backgrounds: Sauter pulse and oscillating electric field
Summary
One of the most remarkable phenomena predicted by quantum electrodynamics (QED) is the process of electronpositron pair production in strong external fields [1,2,3,4]. In a constant uniform electric field E0, the probability of this striking phenomenon is proportional to expð−πEc=E0Þ, where Ec 1⁄4 m2c3=ðjejħÞ ≈ 1.3 × 1016 V=cm is a critical (Schwinger) value of the electric field strength. This fundamental process cannot be described by means of perturbation theory.
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