Non-local corrections to the Dirac equation

The Dirac equation is not semisimple. We therefore construct it as a contraction of a simple theory. The underlying simple structure is necessarily purely algebraic and non-local. It consists of many isomorphic distinguishable qubits with Clifford-Wilczek statistics and spin h̄/2, having a Clifford algebra with 6N generators as algebra of observables. The quantum imaginary ih̄ arises as the vacuum value of a dynamical variable, whose back-reaction provides the Dirac mass. On operational grounds the non-locality is ∼ 10 sec and the associated mass is about the Higgs mass. The simplified Dirac equation is exactly Lorentz invariant but has the symmetry group SO(3, 3) instead of the Poincaré group, and has a non-standard small but unique spin-orbit coupling ∼ 1/N , whose observation would be some evidence for the simpler theory. All the fields of the Standard Model call for similar non-local simplification. PACS numbers: 12.60.-i, 12.10.-g