Quantum-mechanical description of optical beams

TL;DR

This paper develops a quantum-mechanical framework for optical beams based on photon representations from Poincaré group theory, clarifying polarization and wave-particle duality.

Contribution

It introduces a photon-based quantum description of optical beams, emphasizing helicity as fundamental and linking polarization to helicity state combinations.

Findings

Photon properties fully determine light beam characteristics

Polarization arises from helicity state combinations

Provides a rigorous quantum foundation for wave-particle duality

Abstract

Quantum mechanics of photons is derived from the theory of representations of the Poincar\'e group developed by Wigner. This theory places helicity as the most fundamental property; angular momentum and polarization are secondary characteristics. The properties of the beams of light are shown to be fully determined by the quantum states of the photons. Polarization of light beams is explained as the freedom to chose an arbitrary combination of the helicity states. Quantum mechanics of photons enables one to give a precise meaning to the concept of wave-particle duality.