How to generate families of spinors

TL;DR

This paper introduces a universal method using Clifford algebra to generate and transform between different families of spinors across all dimensions and signatures, potentially illuminating the structure of quark and lepton families.

Contribution

It develops a new technique to construct and relate spinor families via Clifford algebra objects, applicable universally across dimensions and signatures.

Findings

Transformation between spinor families is mathematically consistent.

Method applies to all spacetime dimensions and signatures.

Potential implications for understanding particle families.

Abstract

Using a technique \cite{holgernorma2002} to construct a basis for spinors and ``families'' of spinors in terms of Clifford algebra objects, we define other Clifford algebra objects, which transform the state of one ''family'' of spinors into the state of another ''family'' of spinors, changing nothing but the ''family'' number. The proposed transformation works - as does the technique - for all dimensions and any signature and might open a path to understanding families of quarks and leptons\cite{norma92,norma93,normaixtapa2001,pikanorma2002}.