A Unified Understanding of Spin and Orbital Angular Momentum in the Complex Plane

AbstractThe quantum mechanical operator for angular momentum is trans-formed from the real plane into the complex plane. In doing so, theCauchy-Riemann (C-R) equations are interpreted as constraint conditionsdefining two distinct domains where complex differentiation is permitted.It is shown each of these domains contains an orbital angular momentumcontribution plus an non-orbital term that cancels out between them. It isfurther shown the field equations for spinning quantum particles includeC-R equations that restrict the particles to a single complex constraintspace. It is therefore proposed the non-orbital term in the constraint spaceangular momentum is the source of the spin. 1 Introduction Newman [1] has suggested spin angular momentum has a geometrical inter-pretation as a projection of dynamical properties of quantum particles fromcomplex space into real space. The purpose of this paper is to further developthis idea using a direct transformation of the quantum mechanical operator Lˆ