Nonlinear dynamics of a charged particle in a strong non-null knot wave background

TL;DR

This paper investigates the classical and quantum dynamics of a charged particle in a strong electromagnetic knot wave background, revealing new insights into particle trajectories, effective mass, radiation, and quantum scattering processes.

Contribution

It introduces a comprehensive analysis of particle behavior in a non-null knot wave background, including classical solutions and quantum field theory formulations, which is novel in the study of electromagnetic knots.

Findings

Derived particle trajectories and effective mass in the knot wave background

Calculated Volkov solutions and S-matrix for the quantum system

Identified conditions where transition amplitudes are identical for different states

Abstract

In this paper, we study the dynamics of the charged particle interacting with the non-null electromagnetic knot wave background. We analyse the classical system in the Hamilton-Jacobi formalism and find the action, the linear momentum and the trajectory of the particle. Also, we calculate the effective mass and the emitted radiation along the knot wave. Next, we quantize the system in the classical strong knot wave background by using the strong-field QED canonical formalism. We explicitly construct the Furry picture and calculate the Volkov solutions of the Dirac equation. As an application, we discuss the one-photon Compton effect where we determine the general form of the $S$-matrix. Also, we discuss in details the first partial amplitudes in the transition matrix in two simple backgrounds and show that there is a pair of states for which these amplitudes are identical.