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Description
Spin is one of the intrinsic properties of the fundamental particles. Yet we know very little about the fundamental origin of spin. The model of an electron as a spinning charged sphere, which could explain its magnetic moment, does not work due to its clash with the special theory of relativity. As such, we accept the formulation of spin based on the Dirac equation. But it is experimentally known that spin exists even in non-relativistic quantum physics.
In this work, we explore the origin of spin using a semi-classical model of the angular momentum field. From the fact that the angular momentum can be expressed as the angular gradient of classical action, we deduce a wave equation in angular space, in which the spin can be viewed as the source charge of the angular momentum field. We further use it to deduce the spin quantum number for particles and fields. Finally, we check consistency with known experimental results and theoretical formulation.
