The angular momentum of electron radiation in a uniform magnetic field

TL;DR

This paper provides a quantum electrodynamics analysis of the angular momentum of radiation emitted by a relativistic electron in a magnetic field, revealing discrepancies between classical and quantum calculations and proposing a canonical tensor approach.

Contribution

It introduces a quantum theoretical framework for calculating the angular momentum of electron radiation and clarifies the classical limit using the canonical energy-momentum tensor.

Findings

Exact expressions for photon emission probability with angular momentum are derived.

Classical asymptotics do not match the angular momentum flux density from the symmetrized tensor.

Using the canonical energy-momentum tensor aligns quantum results with classical limits.

Abstract

We study theoretically by means of quantum electrodynamics the vortex radiation of a relativistic electron in a uniform magnetic field. The exact expressions for the probability of emission of a photon with a certain angular momentum are found. The classical asymptotics $\hbar\to 0$ of this probability does not match the angular momentum flux density calculated by the classical method using the symmetrized energy-momentum tensor. Although the flux of angular momentum integrated over the radiation directions is the same in both cases. We found the angular momentum flux of the radiation field using the canonical (not symmetrized) energy-momentum tensor and showed that the flux obtained in this way coincide with the classical limit for the probability of photon emission.