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

The 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 that treats the external field to all orders and is based on the solutions of the Dirac equation with the Feynman- or anti-Feynman boundary conditions. The asymptotic properties of those solutions are linked to the electron and positron spin-resolved probability amplitudes of created pairs. The same concerns the helicity-resolved amplitudes. Most importantly, the corresponding spin- or helicity-resolved distributions, 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, i.e., the Dirac-Heisenberg-Wigner function approach or the spinorial one. In contrast to those approaches, however, the $S$-matrix method allows us to investigate the vortex structures in momentum distributions of produced particles, as it provides 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.