Relativistic Spin-Orbit Interactions of Photons and Electrons

TL;DR

This paper investigates how Lorentz boosts affect the spin and orbital angular momentum of photons and electrons, revealing complex spin-orbit interactions crucial for understanding relativistic scattering and emission processes.

Contribution

It provides a detailed analysis of the Lorentz transformation effects on spin and orbital angular momentum in relativistic particles, highlighting the nontrivial spin-orbit conversion phenomena.

Findings

Transverse Lorentz boosts induce spin-to-orbital angular momentum conversion.

The spin, intrinsic, and extrinsic orbital parts transform differently under boosts.

Complex behavior ensures proper Lorentz transformation of total angular momentum.

Abstract

Laboratory optics, typically dealing with monochromatic light beams in a single reference frame, exhibits numerous spin-orbit interaction phenomena due to the coupling between the spin and orbital degrees of freedom of light. Similar phenomena appear for electrons and other spinning particles. Here we examine transformations of paraxial photon and relativistic-electron states carrying the spin and orbital angular momenta (AM) under the Lorentz boosts between different reference frames. We show that transverse boosts inevitably produce a rather nontrivial conversion from spin to orbital AM. The converted part is then separated between the intrinsic (vortex) and extrinsic (transverse shift or Hall effect) contributions. Although the spin, intrinsic-orbital, and extrinsic-orbital parts all point in different directions, such complex behavior is necessary for the proper Lorentz transformation of the total AM of the particle. Relativistic spin-orbit interactions can be important in scattering processes involving photons, electrons, and other relativistic spinning particles, as well as when studying light emitted by fast-moving bodies.