Sixfold Discrete Symmetry Explains Dark Matter

Abstract

Using the Pauli algebra version of the Dirac equation we show the existence of its six symmetric versions whose solutions are referred to as the six sectors of fermion fields. It is shown that the sectors are distinct, by showing that if a fermion field belongs to two sectors at once then its mass must be zero. Also shown is the lack electromagnetic interaction between different sectors, since each sector has its own unique matrix coupling its fermion field to its EM field. 

Altogether this predicts the ratio of dark matter to ordinary matter of 5 to 1, which is close to the observed ratio of 5.2 to 1 [3]. In order to fully justify this prediction, the sixfold discrete symmetry must first of all be extended to the electroweak sector, then to strong interactions. This article only deals with coupling of fermion fields to electromagnetic fields. 

This paper essentially depends on the full equivalence of the Pauli algebra version of the Dirac equation with its standard version, which is proven in (2.1). The sixfold symmetry can be seen in the Pauli algebra version of the Dirac equation, but is harder to see in its standard version.