All fundamental fermions fit inside one su(1|5) irreducible representation

TL;DR

This paper proposes a mathematical framework using the su(1|5) superalgebra to unify all fundamental fermions of one generation within a single irreducible representation, aligning with the Standard Model classification.

Contribution

It introduces a novel su(1|5) representation that accommodates all fundamental fermions and reproduces their Standard Model classification through branching rules.

Findings

All fundamental fermions fit into one su(1|5) irreducible representation.

The branching reproduces the Standard Model fermion classification.

A simple construction of relevant representations is provided.

Abstract

We present the mathematical framework for a unified theory based upon su(1|5). The Lie superalgebra su(1|5) has irreducible representations of dimension 32, in which the 32 fundamental fermions of one generation (leptons and quarks, of left and right chirality, and their antiparticles) can be accommodated. The branching of these su(1|5) representations with respect to its subalgebra su(3) x su(2) x u(1) reproduces precisely the classification of these fundamental fermions according to the gauge group of the Standard Model. Furthermore, a simple construction of the relevant representations is given, and some consequences are discussed.