Temporal Klein Model for Particle-Pair Creation

This work considers the creation of electron-positron pairs from intense electric fields in vacuum, for arbitrary temporal field variations. These processes can be useful to study quantum vacuum effects with ultra-intense lasers. We use the quantized Dirac field to explore the temporal Klein model. This model is based on a vector potential discontinuity in time, in contrast with the traditional model based on a scalar potential discontinuity in space. We also extend the model by introducing a finite time-scale for potential variations. This allows us to study the transition from a singular electric field spike, with infinitesimal duration, to the opposite case of a static field where the Schwinger formula would apply. The present results are intrinsically non-perturbative. Explicit expressions for pair-creation as a function of the potential time-scales are derived. This work explores the spacetime symmetry associated with pair creation in vacuum: the space symmetry breaking of the old Klein paradox model, in contrast with the time symmetry breaking of the temporal Klein model