Chronon corrections to the Dirac equation

Abstract

The Dirac equation is not semisimple. We therefore regard it as a contraction of a simpler decontracted theory. The decontracted theory is necessarily purely algebraic and nonlocal. In one simple model the algebra is a Clifford algebra with 6N generators. The quantum imaginary ℏi is the contraction of a dynamical variable whose backreaction provides the Dirac mass. The simplified Dirac equation is exactly Lorentz invariant but its symmetry group is SO(3, 3), a decontraction of the Poincaré group, and it has a slight but fundamental nonlocality beyond that of the usual Dirac equation. On operational grounds the nonlocality is ∼10−25 s in size and the associated mass is about the Higgs mass. There is a nonstandard 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 nonlocal simplification.