Nonperturbative Description Of The Mass And Charge Renormalization In Quantum Electrodynamics

TL;DR

This paper presents a nonperturbative analysis of electron-positron field excitations in QED, deriving finite charge and mass renormalizations and connecting theoretical parameters with observed physical constants.

Contribution

It introduces a variational approach to derive finite renormalization of electron charge and mass in nonperturbative QED, linking bare parameters with physical observables.

Findings

Finite renormalization of charge and mass obtained.

Connection between bare parameters and observed constants.

Relativistic spectrum of the physical electron confirmed.

Abstract

In this paper the nonperturbative analysis of the spectrum for one-particle excitations of the electron-positron field (EPF) is considered in the paper. A standard form of the quantum electrodynamics (QED) is used but the charge of the "bare" electron $e_0$ is supposed to be of a large value. It is shown that in this case the quasi-particle can be formed with a non-zero averaged value of the scalar component of the electromagnetic field (EMF). Self-consistent equations for the distribution of charge density in the "physical" electron (positron) are derived. A variational solution of these equations is obtained and it defines the finite renormalization of the charge and mass of the electron (positron). It is found that the coupling constant between EPF and EMF and mass of the "bare" electron can be connected with the observed values of the fine structure constant and the mass of the "physical" electron. It is also shown that although the non-renormalized QED corresponds to the strong coupling between EPF and EMF, the interaction between "physical" electron (positron) with EMF is defined by the observed value of the coupling constant. It is proved that the translational motion of the "physical" particle is separated from its internal degrees of freedom. As a result the dependence of the one-particle excitation energy on its total momentum corresponds to the relativistic spectrum of a free particle with the observed value of mass. Regularization of the terms of a series of the perturbation theory is due to the form-factor of the "physical" electron (positron).