Triality and Quantization of Singularities in Massive Fermion

TL;DR

This paper demonstrates how fermions can gain mass via a special vector potential linked to triality in Dirac spinors, leading to quantization conditions for physical constants including mass.

Contribution

It introduces a novel vector potential related to triality, showing its role in fermion mass generation and quantization of physical constants.

Findings

Fermions acquire mass through a non-integrable exponential factor.

The phase change around singularities leads to quantization of physical constants.

Massive Dirac equation in bosonic form is self-dual.

Abstract

It is proved that fermions can acquire the mass through the additional non-integrable exponential factor. For this propose the special vector potential associated with the spinor field was introduced. Such a vector potential has close relation with the triality property in Dirac spinors and plays crucial role in the construction of massive term. It is shown that the change in phase of a wavefunction round any closed curve with the possibility of there being singularities in our vector potential will lead to the law of quantization of physical constants including the mass. The triality properties of Dirac's spinors are studied and it leads to a double covering vector representation of Dirac spinor field. It is proved that massive Dirac equation in the bosonic representation is self-dual.