The mass shift of an electron in an electric field and its connection with the infrared problem in QED

Abstract

Abstract The main purpose of this talk is to acquaint the audience with interesting properties of the mass shift of electron in a homogeneous constant field, especially with its classical asymtotics arising at small quantum parameters (2), when β1,β2, χ≪1. The unusual properties of this shift are: classicity and at the same time its absence in classical Abraham-Lorentz-Dirac equation; nonlocality expressing formation on the length ∼mc 2/eϵ much greater than Compton length h/mc; linearity in the modulus of eϵ, i.e. nonanalyticity and, consequently, nonperturbativity in the external field ϵ independence of spin of a particle but dependence on spin of proper field. Although the shift does not change the classical equation of motion, it does alter the action and should therefore manifest itself in quantum-mechanical processes. For example, in pair creation by electric field in vacuum described by imaginary part of Lagrange function of external field. It is shown also that due to locality, causality and unitar...