Volume 11, Issue 4, pages 560-571
This work explores a geometric interpretation of the Dirac spinor based on toroidal excitation within a neutral, scalar field. The model derives the Dirac operator from the energy density and spatial gradient of the scalar field, reconstructing the fermion Lagrangian without invoking gamma matrices. The rest mass arises from internal zitterbewegung constrained by the toroidal geometry and can be generated via a Yukawa coupling. Forward momentum is linked to the spatial propagation rate of the scalar field excitation. The framework introduces both global and local gauge-like symmetries arising from phase variation in the scalar field, suggesting that spinor behavior and gauge interactions may emerge from a deeper scalar field structure. This geometric approach offers a deterministic foundation for spin-½ dynamics and a novel path toward unifying spinor fields with scalar field. The Schrodinger operators emerge from toroidal dynamics of scalar field. This can potentially lead to a unified Lagrangian and it has the potential to solve cosmological constant problem.
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