Unified theory for external and internal attributes and symmetries of fundamental fermions

TL;DR

This paper proposes a unified algebraic framework for describing the external space-time and internal symmetries of fundamental fermions, offering new insights into their attributes and interactions.

Contribution

It introduces a novel algebraic structure based on triple-direct-products of gamma matrices and a triplet spinor-field to unify fermion attributes and symmetries.

Findings

Derivation of Dirac mass matrices with quasi-democratic structure

Natural qualification of Yukawa interactions within the formalism

Identification of three commutative sub-algebras for different symmetries

Abstract

An unorthodox unified theory is developed to describe external and internal attributes and symmetries of fundamental fermions, quarks and leptons. Basic ingredients of the theory are an algebra which consists of all the triple-direct-products of Dirac gamma-matrices and a triple-spinor-field, called a triplet field, defined on the algebra. The algebra possesses three commutative sub-algebras which describe, respectively, the external space-time symmetry, the family structure and the internal color symmetry of quarks and leptons. The triplet field includes threefold (fourfold) repetitionary modes of spin 1/2 component fields with SU(3) (SU(4)) color symmetry. It is possible to qualify the Yukawa interaction and to make a new interpretation of its coupling constants naturally in an intrinsic mechanism of the triplet field formalism. The Dirac mass matrices with quasi-democratic structure are derived as an illustration.