Classical renormalization and the Dirac equation

The mass-density i/r (x, t)y0trn/r(x, t) defines an invariant mass integral for the Dirac field, 

In quantized theory, this is an operator in the fermion field algebra. Assuming mo = 0, the mean value (0 Af 0) vanishes in the reference vacuum state because all momenta and currents cancel out. In a single-electron state a) = al 0), a self-energy (more precisely, self-mass) is defined by Smc2 = a Mc2 a) = a / d3x y0(—eji)i/ a). Only helicity-breaking virtual transitions can contribute to this electromagnetic self-mass. 

The field equation for a free dressed electron is (p — m) f = 0, in units such that ti = c = 1. The space-time Green function Gm(xi, xo) for this field equation 

---