Vacuum polarization and pair production in time-dependent electric fields: A quantum-kinetic-equation approach

The evolution of the vacuum state in a time-dependent external electric field of arbitrary polarization is investigated within a nonperturbative framework of quantum kinetic equations (QKEs). In our previous work [], a revised version of the QKEs was derived by using an adiabatic basis constructed from one-particle Hamiltonian eigenfunctions in a spatially homogeneous electric field. In this study, we present an extensive analysis of these equations with particular emphasis on observable quantities. The focus of the present work is therefore not on a rederivation of asymptotic pair-production spectra for special pulses, but on a self-contained construction of basis-independent observables and their renormalization in a matrix-valued QKE formulation valid for arbitrary polarization. Specifically, we compute momentum-resolved particle yields, the induced electron-positron current, the energy-momentum tensor, and the angular-momentum tensor. In the linear-polarization limit these observables reduce to known QKE expressions; here they are constructed explicitly for the corrected QKE system at arbitrary polarization, with circularly polarized fields included as a special case. We also discuss in detail the charge-renormalization procedure required to remove logarithmic divergences. It is shown that our results are consistent with the previous findings obtained via the Dirac-Heisenberg-Wigner formalism. Our analysis provides a firmer theoretical basis for investigations of nonperturbative effects in strong electric fields.