No Charged Higgs: A Geometric Argument - On the Role of Spin in the Origin of Charge

In the standard formulation of quantum mechanics the appearance of the complex unit i is taken as axiomatic.In the framework of geometric algebra, however, i acquires a direct geometric meaning.For fermions it is realized by the bivector of the spin plane, which singles out a spin direction.Electromagnetic coupling then arises naturally as U(1) rotations around this axis.By contrast, a scalar particle lacks such a direction, and the only available representative of i is the spacetime pseudoscalar.This leads to a representation of U(1) that is incompatible with the fermionic case.Our objection is therefore not to the algebraic consistency of minimal coupling, but to its geometric compatibility across particle types.Assuming the universality of electromagnetic interaction, we predict that no elementary electrically charged scalar particles exist.In particular, the charged Higgs sector should not be realized in nature.