Feasibility of Finite Renormalization of Particle Mass in Quantum Electrodynamics

The paper proposes an algorithm for regularization of the self-energy expressions for a Dirac particle that meets the relativistic and gauge invariance requirements. Within the second order formulations of the "old" perturbation theory for free motion, the expression for the upper integration limit q is a slowly enough varying function of particle impulse. For a particle at rest, q = m; for the ultra-relativistic case |p| ≫ m : q ≈ 2m. For 4D perturbation theory, on introduction of the limiting 4-impulse,L² =L_0² -L², it is shown that with a large time component, L₀/m ≫ 1, the spatial values of L_i are limited and are the same as the components of the introduced limits of integration q_i: L² = q². Within the proposed algorithm, in the second-order of the perturbation theory, the renormalized Dirac particle mass is m⁽²⁾ = m₀ + Δm⁽²⁾ = m₀ (1 + 1.115 e²/π) , where m₀ is the bare mass of the particle.