Wigner's Photons

TL;DR

This paper explores Wigner's concept of photons, focusing on the Lorentz-invariant helicity and the gauge degrees of freedom associated with the E(2)-like little group, linking abstract group theory with measurable polarization experiments.

Contribution

It connects the theoretical framework of Wigner's photons and the E(2)-like little group with practical polarization experiments to study gauge degrees of freedom.

Findings

Polarization experiments can probe the E(2)-like little group.

Helicity remains Lorentz-invariant for massless particles.

Gauge degrees of freedom relate to translation-like symmetries.

Abstract

If Einstein's photon is $E = cp = \hbar\omega$, Wigner's photon is its helicity which is a Lorentz-invariant concept coming from the E(2)-like little group for massless particles. In addition, the E(2)-like little group has two translation-like degrees of freedom. What happens to them? They are associated with the gauge degree of freedom. Since the physics of polarized light waves can be formulated within the framework of the Lorentz group, it is now possible to use polarization experiments to study the E(2)-like little group in terms of quantities that can be measured in laboratories.