Rotating light, OAM paradox and relativistic complex scalar field

TL;DR

This paper introduces a covariant scalar field approach to analyze the orbital angular momentum of rotating light beams, resolving paradoxes and clarifying the physical interpretation within a relativistic framework.

Contribution

It presents a novel covariant formalism using complex scalar fields to accurately compute orbital angular momentum in rotating light, resolving existing paradoxes.

Findings

Orbital angular momentum aligns with rigid rotation for modes with opposite azimuthal indices.

Proper accounting eliminates paradoxical interpretations of rotating light's angular momentum.

The formalism connects gauge currents with Poynting vector continuity in a relativistic setting.

Abstract

Recent studies show that the angular momentum, both spin and orbital, of rotating light beams possesses counter-intuitive characteristics. We present a new approach to the question of orbital angular momentum of light based on the complex massless scalar field representation of light. The covariant equation for the scalar field is treated in rotating system using the general relativistic framework. First we show the equivalence of the U(1) gauge current for the scalar field with the Poynting vector continuity equation for paraxial light, and then apply the formalism to the calculation of the orbital angular momentum of rotating light beams. If the difference between the co-, contra-, and physical quantities is properly accounted for there does not result any paradox in the orbital angular momentum of rotating light. An artificial analogue of the paradoxical situation could be constructed but it is wrong within the present formalism. It is shown that the orbital angular momentum of rotating beam comprising of modes with opposite azimuthal indices corresponds to that of rigid rotation. A short review on the electromagnetism in noninertial systems is presented to motivate a fully covariant Maxwell field approach in rotating system to address the rotating light phenomenon.