# Dirac states of an electron in a circular intense magnetic field

## TL;DR

This paper models Dirac electron states in intense, curved magnetic fields relevant to neutron-star magnetospheres, extending Landau states to curved geometries and setting the stage for analyzing quantum curvature radiation.

## Contribution

It introduces a theoretical framework for Dirac particles in curved magnetic fields, generalizing Landau states to curved geometries in neutron-star environments.

## Key findings

- Derived Dirac states in curved magnetic fields with small Larmor radius.
- Connected curved magnetic field states to relativistic Landau states as a limit.
- Laid groundwork for future analysis of quantum curvature radiation.

## Abstract

Neutron-star magnetospheres are structured by very intense magnetic fields extending from 100 to 10 5 km traveled by very energetic electrons and positrons with Lorentz factors up to $\sim$ 10 7. In this context, particles are forced to travel almost along the magnetic field with very small gyro-motion, potentially reaching the quantified regime. We describe the state of Dirac particles in a locally uniform, constant and curved magnetic field in the approximation that the Larmor radius is very small compared to the radius of curvature of the magnetic field lines. We obtain a result that admits the usual relativistic Landau states as a limit of null curvature. We will describe the radiation of these states, that we call quantum curvature or synchro-curvature radiation, in an upcoming paper.