Incompatibility of the tunneling limit with laser fields

The Schwinger limit refers to longitudinal electric fields that are sufficiently s to “polarize the vacuum” into electron-positron pairs by a tunneling mechanism. Laser fields are transverse electromagnetic fields for which the Schwinger limit has no relevance. Longitudinal and transverse fields are fundamentally different because of the different values of the F µ� Fµ� Lorentz invariant that characterizes the fields. One aspect of this difference is the zero-frequency limit, that exists for longitudinal fields, but is ill-defined for transverse fields. The goal of approaching the Schwinger limit with sufficiently strong lasers is thus not a possibility. Tunneling transition rates are characterized by an exponential behavior of the form exp(−C/E), where E is the magnitude of the applied electric field and C is a system-dependent constant. Searches for such behavior within a Coulomb-gauge treatment of laser-induced processes are shown to fail.