# Quantum theory of curvature and synchro-curvature radiation in a strong and curved magnetic field, and applications to neutron star magnetospheres

## TL;DR

This paper develops a quantum theoretical framework for curvature and synchro-curvature radiation in strong, curved magnetic fields, with applications to neutron star magnetospheres, bridging classical and quantum descriptions of particle radiation.

## Contribution

It extends previous work by deriving quantum radiation from Dirac particles in curved magnetic fields, introducing discrete transitions and quantum recoil corrections.

## Key findings

- Classical curvature radiation is recovered within the quantum framework.
- Quantum synchro-curvature radiation expressions are derived.
- Quantum recoil and deconfinement corrections are formulated.

## Abstract

In a previous paper, we derived the quantum states of a Dirac particle in a circular, intense magnetic field in the limit of low momentum perpendicular to the field with the purpose of giving a quantum description of the trajectory of an electron, or a positron, in a typical pulsar or magnetar magnetosphere. Here we continue this work by computing the radiation resulting from transitions between these states. This leads to derive from first principles a quantum theory of the so-called curvature and synchro-curvature radiations relevant for rotating neutron-star magnetospheres. We find that, within the approximation of an infinitely confined wave-function around the magnetic field and in the continuous energy-level limit, classical curvature radiation can be recovered in a fully consistent way. Further we introduce discrete transitions to account for the change of momentum perpendicular to the field and derive expressions for what we call quantum synchro-curvature radiation. Additionally, we express deconfinement and quantum recoil corrections.