How Clifford algebra helps understand second quantized quarks and leptons and corresponding vector and scalar boson fields, {\it opening a new step beyond the standard model}

TL;DR

This paper uses Clifford algebra to describe internal spaces of fermions and bosons in higher dimensions, revealing how their properties relate to observed particles and gauge fields, and making new predictions beyond the standard model.

Contribution

It introduces a Clifford algebra framework for internal spaces that unifies fermion and boson properties and extends to higher dimensions, predicting new particle features.

Findings

Clifford odd basis vectors relate to fermion properties and families.

Clifford even basis vectors relate to gauge fields.

Higher-dimensional creation operators reproduce observed particle properties.

Abstract

This article presents the description of the internal spaces of fermion and boson fields in $d$-dimensional spaces, with the odd and even "basis vectors" which are the superposition of odd and even products of operators $\gamma^a$. While the Clifford odd "basis vectors" manifest properties of fermion fields, appearing in families, the Clifford even "basis vectors" demonstrate properties of the corresponding gauge fields. In $d\ge (13+1)$ the corresponding creation operators manifest in $d=(3+1)$ the properties of all the observed quarks and leptons, with the families included, and of their gauge boson fields, with the scalar fields included, making several predictions. The properties of the creation and annihilation operators for fermion and boson fields are illustrated on the case $d=(5+1)$, when $SO(5,1)$ demonstrates the symmetry of $SU(3)\times U(1)$.