Repairing the algebraic foundations of the Standard Model of particle physics

Abstract

The Standard Model (SM) of particle physics is in such good agreement with experiment that it is still accepted as providing an accurate model of reality. Nevertheless, its algebraic foundations are in need of repair. Chirality is shown to be algebraically inconsistent with neutrinos having finite mass and being fermions. The SM description of parity is shown to be inconsistent, leading to erroneous interpretations of experiments, notably parity non-conservation. It is shown that a correct description of the intrinsic parity of fermions can only be obtained by extending the $Cl_{1,3}$ Dirac algebra at least to $Cl_{2,3}$. The $Cl_{3,3}$ algebra is shown to provide a description of parity that is always conserved and establishes a relation between spin direction and parity in the weak interaction, identifying the $σ$ matrices of the weak potential with its elements.