Schwinger pair creation with the backreaction in 3 + 1 dimensions

In this work, I analyze the structure of the QED spacetime lattice and review the Schwinger pair creation process from a thermodynamic point of view. This viewpoint enables the dynamical mean-field calculation for the 3 + 1 dimensional Schwinger pair creation with the backreaction. As an example, I demonstrate how to evaluate the pair creation in a finite volume with external electric fields turned on at $t=0$. The numerical results show how the backreaction responds to the external fields and influences the pair creation.