Consistency restrictions on maximal electric field strength in QFT

TL;DR

This paper derives restrictions on the strength and duration of external electric fields in quantum field theory to ensure backreaction remains small, based on analyzing energy density contributions from particle creation.

Contribution

It provides new consistency conditions on electric field parameters in QED and QCD by analyzing energy density asymptotics for finite-time fields.

Findings

Restrictions on electric field strength and duration derived

Backreaction effects are quantified and constrained

Time scales for electric field depletion established

Abstract

QFT with an external background can be considered as a consistent model only if backreaction is relatively small with respect to the background. To find the corresponding consistency restrictions on an external electric field and its duration in QED and QCD, we analyze the mean energy density of quantized fields for an arbitrary constant electric field E, acting during a large but finite time T. Using the corresponding asymptotics with respect to the dimensionless parameter $eET^2$, one can see that the leading contributions to the energy are due to the creation of paticles by the electric field. Assuming that these contributions are small in comparison with the energy density of the electric background, we establish the above-mentioned restrictions, which determine, in fact, the time scales from above of depletion of an electric field due to the backreaction