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

For semiclassical electrodynamics to be an accurate approximation, quantum fluctuations must be small. The validity of the semiclassical approximation in 1+1 electrodynamics has been investigated using a criterion which involves the stability of solutions to the linear response equation, which is found by perturbing the semiclassical backreaction equation. If the solutions grow rapidly in time, then the criterion states that the semiclassical approximation breaks down. Numerical solutions to the linear response equation will be presented for the case of an electric field that is coupled to a homogeneous classical electric current and, through the semiclassical approximation, the current due to a quantized spin 1/2 field in a homogeneous state. The focus of this talk will be on the impact quantum fluctuations have on solutions to the linear response equation in the context of the above validity criterion.