Photon emission due to vacuum instability under the action of a quasi-constant electric field

Following a nonperturbative formulation of strong-field QED developed in our earlier works, we consider photon emission accompanying vacuum instability under the action of a quasi-constant strong electric field of finite duration $T$. We construct closed formulas for the total probabilities and study the photon emission accompanying electron–positron pair creation from the vacuum. We establish the domain of applicability of the locally constant field approximation (LCFA) for the photon emission. We study angular and polarization distribution of the emission as well as emission characteristics in a high-frequency approximation with respect of $1/T$. The results presented in this work are suitable to a further development of the LCFA proposed in [Phys. Rev. D, 95, 076013 (2017)].