Bundle Theoretic Descriptions of Massless Single-Particle State Spaces; Gauge Freedom

Abstract

Recently, a bundle theoretic description of massive single-particle state spaces, which is better suited for Relativistic Quantum Information Theory than the ordinary Hilbert space description, has been suggested. However, the mathematical framework presented in that work does not apply to massless particles. It is because, unlike massive particles, massless particles cannot assume the zero momentum state and hence the mass shell associated with massless particles has nontrivial cohomology. More precisely, the helicities of massless particles, which are shown to be equal to the first Chern classes of the bundles associated with the particles, act as topological obstructions that prevent us from applying the same framework. To overcome this difficulty, this paper suggests a new framework that applies to massless particles. Applications to the cases of massless particles with spin-1 and 2, namely the photon and the graviton, will reveal that the field equations, the gauge conditions, and the gauge freedoms of Electromagnetism and General Relativity naturally arise as manifestations of an inertial observer's perception of internal quantum states of a photon and a graviton, respectively. Finally, we show that gauge freedom is exhibited by all massless particles, except those with spin-0 and 1/2.