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From previous work arXiv:2010.09811, the semiclassical backreaction equationin 1+1 dimensions was solved and a criterion was implemented to assess thevalidity of the semiclassical approximation in this case. The criterioninvolves the behavior of solutions to the linear response equation whichdescribes perturbations about solutions to the semiclassical backreactionequation. The linear response equation involves a time integral over atwo-point correlation function for the current induced by the quantum field andit is expected that significant growth in this two-point function (andtherefore in quantum fluctuations) will result in significant growth insolutions to the linear response equation. It was conjectured for early timesthat the difference of two nearby solutions to the semiclassical backreactionequation, with similar initial conditions, can act as an approximate solutionto the linear response equation. A comparative analysis between the approximateand numerical solutions to the linear response equation, for the critical scalefor particle production, will be presented for the case of a massive, quantizedspin 1/2 field in order to determine how robust the approximation method is forrepresenting its solutions.

Validity of the Semiclassical Approximation in 1+1 Electrodynamics: Numerical Solutions to the Linear Response Equation