Renormalization in Lorentz-Abraham-Dirac Equation, Describing Radiation Force in Classical Electrodynamics (in Russian)

TL;DR

This paper explores different renormalization choices for the electron's 4-momentum in the Lorentz-Abraham-Dirac equation, leading to new, well-founded equations that avoid run-away solutions and are applicable to ultra-bright laser scenarios.

Contribution

It introduces a novel renormalization approach that treats the electron's mass as an operator or tensor, resulting in equations with well-defined energy-momentum relations.

Findings

Traditional renormalization leads to non-positive definite energy.

Alternative approach ensures positive energy and well-defined momentum.

New equations are simpler and suitable for laser particle simulations.

Abstract

While he derived the equation for the radiation force, Dirac (1938) mentioned a possibility to use different choices for the 4-momentum of an emitting electron. Particularly, the 4-momentum could be non-colinear to the electron 4-velocity. This ambiguity in the electron 4-momentum allows us to assume that the mass of emitting electron may be an operator, or, at least, a 4-tensor instead of being the usually assumed scalar, which relates the 4-velocity of a bare charge to the total momentum of a dressed point electron, the latter being a total of the momentum of the bare electron and that of the own electromagnetic field. On applying the re-normalization procedure to the mass operator, we arrive at an interesting dichotomy. The first choice (more close to traditional one) ensures the radiation force to be orthogonal to the 4-velocity. In this way the re-normalization results in the Lorentz-Abraham-Dirac equation or in the Eliezer equation. However, the 4-momentum of electron in this case is not well defined: the equality in the relativistic entity (E/c)^2=m^2c^2+p^2 appears to be broken and even the energy is not definite positive. The latter is an underlying reason for the 'run-away' solution. The other choice is to require the radiation force to be orthogonal to the 4-momentum (not to the 4-velocity). In this case the energy and momentum are well-defined and obey the relationship (E/c)^2=m^2c^2+p^2. Remarkably, the equations of a particle's motion in this case differ significantly from all the known versions. They appear to be well founded. They are simple, easy to solve, and can be applied to simulate the particle motion in the focus of an ultra-bright laser.