Majorana's stellar representation for the local polarization of harmonic electromagnetic and gravitational waves

TL;DR

This paper introduces the Majorana stellar representation to analyze the local polarization of electromagnetic and gravitational waves, emphasizing measurement-based observations and the benefits of dual-symmetric detectors.

Contribution

It presents a novel application of the Majorana stellar representation to wave polarization, linking it to measurable quantities and detector sensitivity.

Findings

Majorana representation provides a clear physical interpretation of wave polarization.

Dual-symmetric detectors enhance the measurement of wave properties.

Expressions for energy, momentum, helicity, and spin densities are derived in this framework.

Abstract

The local polarization of electromagnetic (EMW) and gravitational waves (GW) is discussed from an operational point of view, in which all the relevant mathematical framework is constructed in terms of measurements of the power absorbed by a local detector. The intrinsic dependence of the observations upon the nature of the detector is emphasized. In particular, the benefit of using a dual-symmetric detector, equally sensitive to the electric and magnetic fields of the EMW (resp. gravito-electric and gravito-magnetic tensor in the GW case) is pointed out. The Majorana stellar representation of the polarization is introduced, and its physical interpretation is highlighted. Finally, expressions for the energy density, linear momentum density, helicity and spin density of the wave in terms of the Majorana representation are presented.