Schwinger Pair Production at Finite Temperature

Thermal corrections to Schwinger pair production are potentially important in particle physics, nuclear physics and cosmology. However, the lowest-order contribution, arising at one loop, has proved difficult to calculate unambiguously. We show that this thermal correction may be calculated for charged scalars using the worldline formalism, where each term in the decay rate is associated with a worldline instanton. We calculate all finite-temperature worldline instantons, their actions and fluctuations prefactors, thus determining the complete one-loop decay rate at finite temperature. The thermal contribution to the decay rate becomes nonzero at a threshold temperature $T=eE/2m$, above which it dominates the zero temperature result. This is the lowest of an infinite set of thresholds at $T=neE/2m$. The decay rate is singular at each threshold as a consequence of the failure of the quadratic approximation to the worldline path integral. We argue that that higher-order effects will make the decay rates finite everywhere, and model those effects by the inclusion of hard thermal loop damping rates. We also demonstrate that the formalism developed here generalizes to the case of finite-temperature pair production in inhomogeneous fields.