Scattering matrix approach to dynamical Sauter-Schwinger process: Spin- and helicity-resolved momentum distributions

Dynamical Sauter-Schwinger mechanism of electron-positron pair creation by a time-dependent electric field pulses is considered using the $S$-matrix approach and reduction formulas. They lead to the development of framework based on the solutions of the Dirac equation with the Feynman- or anti-Feynman boundary conditions. Their asymptotic properties are linked to the spin-resolved probability amplitudes of created pairs. The same concerns the helicity-resolved amplitudes. Most importantly, the aforementioned spin- or helicity-resolved amplitudes, when summed over spin or helicity configurations, reproduce the momentum distributions of created particles calculated with other methods that are typically used in this context. This does validate the current approach. It also allows us to investigate the vortex structures in momentum distributions of produced particles, as the method provides an access to the phase of the probability amplitude. As we also illustrate numerically, the method is applicable to arbitrary time-dependent electric fields with, in general, elliptical polarization. This proves its great flexibility.