On the geometry and topology of the angular momentum of light

Abstract

The classical field theory approach to the angular momentum of light, specifically how it represents the spin angular momentum of light, has been a matter of controversy for some time. This thesis analyses the aforementioned approach from the point of view of the Exterior Calculus and de Rham Cohomology. It is found purely mathematically that the spin angular momentum of a circularly polarized plane wave of light must be identically zero. It is concluded that the classical formulation of the angular momentum of a plane wave of light is, on some level, incomplete.