Isotopic liftings of Clifford algebras and applications in elementary particle mass matrices

TL;DR

This paper develops isotopic liftings of Clifford algebras using a new product with an isounit, applying the formalism to model quark mass matrices and flavor symmetries in particle physics.

Contribution

It introduces a novel isotopic product in Clifford algebras and applies it to accurately represent quark flavor symmetries and mass matrices in elementary particles.

Findings

Isotopic Clifford algebra formalism models quark flavor symmetry.

The isounit depends on quark masses, linking algebraic structure to physical parameters.

Constraints on parameters align with current quark mass limits.

Abstract

Isotopic liftings of algebraic structures are investigated in the context of Clifford algebras, where it is defined a new product involving an arbitrary, but fixed, element of the Clifford algebra. This element acts as the unit with respect to the introduced product, and is called isounit. We construct isotopies in both associative and non-associative arbitrary algebras, and examples of these constructions are exhibited using Clifford algebras, which although associative, can generate the octonionic, non-associative, algebra. The whole formalism is developed in a Clifford algebraic arena, giving also the necessary pre-requisites to introduce isotopies of the exterior algebra. The flavor hadronic symmetry of the six u,d,s,c,b,t quarks is shown to be exact, when the generators of the isotopic Lie algebra su(6) are constructed, and the unit of the isotopic Clifford algebra is shown to be a function of the six quark masses. The limits constraining the parameters, that are entries of the representation of the isounit in the isotopic group SU(6), are based on the most recent limits imposed on quark masses.