Linear Response Analysis of the Semiclassical Approximation to Spin 1/2 Quantum Electrodynamics in 1+1 Dimensions

TL;DR

This paper examines the validity of the semiclassical approximation in 1+1 dimensional quantum electrodynamics with spin 1/2 particles by analyzing linear response and quantum fluctuations, comparing exact and approximate solutions.

Contribution

It provides a detailed linear response analysis of quantum fluctuations in semiclassical QED, validating approximate solutions against exact ones for specific electric field strengths.

Findings

Exact solutions differ from approximate ones at later times.

Quantum fluctuations influence the stability of the backreaction.

The validity of semiclassical approximation depends on field strength and time.

Abstract

An investigation of the validity of the semiclassical approximation to quantum electrodynamics in 1+1 dimensions is given. The criterion for validity used here involves the impact of quantum fluctuations introduced through a two-point function which emerges naturally when considering the stability of the backreaction equation to linear order perturbations, resulting in the linear response equation. Consideration is given to the case of a spatially homogeneous electric field generated by a classical source, coupled to a quantized massive spin 1/2 field. Solutions to the linear response equation as well as the impact of quantum fluctuations introduced through the current density two-point correlation function are presented for two relevant electric field-to-mass parameter values $qE/m^2$, indicative of the strength of the backreaction process. Previous efforts utilized approximate solutions to the linear response equation that were expected to be valid for early times. A comparative analysis is given between the exact and approximate solutions in order to validate this conjecture.