# A Frenet-Serret Interpretation of Particle Dynamics in High-Intensity Laser Fields

## TL;DR

This paper applies the Frenet-Serret formalism to analyze charged particle trajectories in high-intensity laser fields, connecting geometric properties with quantum and classical effects like radiation reaction and spin precession.

## Contribution

It introduces a geometric framework for understanding particle dynamics in intense laser fields, incorporating quantum effects and radiation reaction beyond traditional models.

## Key findings

- Approximate relations for Frenet-Serret scalars in laser interactions
- Quantum effects emerge when trajectory curvature approaches Compton wavelength
- Simulation results suggest ways to distinguish classical and quantum radiation reaction

## Abstract

In this paper we discuss the dynamics of charged particles in high-intensity laser fields in the context of the Frenet-Serret formalism, which describes the intrinsic geometry of particle worldlines. We find approximate relations for the Frenet-Serret scalars and basis vectors relevant for high-intensity laser particle interactions. The onset of quantum effects relates to the curvature radius of classical trajectories being on the order of the Compton wavelength. The effects of classical radiation reaction are discussed, as well as the classical precession of the spin-polarization vector according to the Thomas-Bargman-Michel-Telegdi (T-BMT) equation. We comment on the derivation of the photon emission rate in strong-field QED beyond the locally constant field approximation, which is used in Monte Carlo simulations of quantum radiation reaction. Such a numerical simulation is presented for a possible experiment to distinguish between classical and quantum mechanical models of radiation reaction.