Quantum-mechanical description of optical beams

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.