# Superintegrable relativistic systems in spacetime-dependent background fields

## TL;DR

This paper explores symmetries in relativistic charged particles within spacetime-dependent electromagnetic fields, identifying conserved quantities and presenting new superintegrable systems with complex integrals of motion.

## Contribution

It introduces a systematic method to identify symmetries and conserved quantities in relativistic systems with spacetime-dependent backgrounds, including novel superintegrable models.

## Key findings

- Identification of symmetries generating conserved quantities
- Examples of superintegrable relativistic systems with quadratic and nonpolynomial integrals
- Extension of integrability concepts to relativistic charged particles in complex fields

## Abstract

We consider a relativistic charged particle in background electromagnetic fields depending on both space and time. We identify which symmetries of the fields automatically generate integrals (conserved quantities) of the charge motion, accounting fully for relativistic and gauge invariance. Using this we present new examples of superintegrable relativistic systems. This includes examples where the integrals of motion are quadratic or nonpolynomial in the canonical momenta.