Spinning Particles 12+

📓 We construct non-relativistic and relativistic non-Grassmann spinning particles on the ground of oldest idea about spin as "intrinsic angular momentum". Spin degrees of freedom live on a fiber bundle with a base parameterized by the inner angular-momentum coordinates. In the relativistic case, configuration space of the spin degrees of freedom is anti-de Sitter space. This produces both gamma-matrices and Lorentz generators in the course of quantization. Canonical quantization of the model implies the Dirac equation. We present the detailed analysis of both the Lagrangian and the Hamiltonian formulations of the model and obtain the general solution to the classical equations of motion. Comparing Zitterbewegung of the spatial coordinate with the evolution of spin, we ask on the possibility of space-time interpretation for the inner space of spin. We enumerate similarities between our analogous model of the Dirac equation and the two-body system subject to confining potential which admits only the elliptic orbits of the order of de Broglie wave-length. The Dirac equation dictates the perpendicularity of the elliptic orbits to the direction of center-of-mass motion.