Renormalization of the fermion-charge due to electromagnetic self-interactions in time-dependent, relativistic quantum mechanics

 The time-dependent electromagnetically self-coupled Dirac equation is solved numerically by means of the MSD2 algorithm with special attention to stability. The expectation values of several dynamic operators are evaluated as functions of time and the asymptotic, i.e., physical values are obtained. These include the fermion dynamic mass, and charge. The dependence of the expectation values on the spatial-grid size is evaluated and yields finite results due to the finiteness and continuity of the spinor. A statistical method, employing a canonical ensemble whose temperature is the inverse of the spatial-grid size, is used to remove the momentum-dependence. A result for each spatial-grid size value is obtained and the continuum limit is taken to calculate the fermion renormalized mass and charge. The charge renormalization is attributed to the contribution of the negative-energy components of the time-dependent Dirac spinors. The renormalization mass correction is 10% and the charge correction is about 5%.