The Validity of the Semiclassical Approximation for Particle Production Due to a Strong Electric Field

In a vacuum, particle production occurs if a strong electric field is present. These particles accelerate and react back on the electric field from which they were produced. The semiclassical approximation, in which the electric field is treated classically, is frequently used to describe this process. The validity of the semiclassical approximation is investigated in scalar electrodynamics where the particle production occurs for a massive charged scalar field. Specifically, the case in which the background electric field turns on from zero at some particular time and then approaches a constant value at late times is considered. Approximate solutions to the linear response equation are computed in order to determine this validity. If quantum fluctuations are large and the semiclassical approximation is therefore invalid, it is expected that solutions to the linear response equation will grow significantly in time.