# Exact classical and quantum dynamics in background electromagnetic fields

## TL;DR

This paper develops exact models for classical and quantum dynamics of particles in complex electromagnetic fields, moving beyond simple plane wave approximations to include realistic laser beam structures.

## Contribution

It introduces a method leveraging Poincaré symmetry and superintegrability to construct and solve new models of laser-particle interactions without approximation.

## Key findings

- Exact classical orbits in a radially polarised laser beam
- Quantum wave functions for particles in complex laser fields
- Enhanced predictive capability for intense laser experiments

## Abstract

Analytic results for (Q)ED processes in external fields are limited to a few special cases, such as plane waves. However, the strong focussing of intense laser fields implies a need to go beyond the plane wave model. By exploiting Poincar\'e symmetry and superintegrability we show how to construct, and solve without approximation, new models of laser-particle interactions. We illustrate the method with a model of a radially polarised (TM) laser beam, for which we exactly determine the classical orbits and quantum wave functions. Including in this way the effects of transverse field structure should improve predictions and analyses for experiments at intense laser facilities.