Can the "basis vectors", describing the internal spaces of fermion and boson fields with the Clifford odd (for fermion) and Clifford even (for boson) objects, explain interactions among fields, with gravitons included?

Abstract

The Clifford odd and even ``basis vectors'', describing the internal spaces of fermion and boson fields, respectively, offer in even-dimensional spaces, like in $d=(13+1)$, the description of quarks and leptons and antiquarks and antileptons appearing in families, as well as of all the corresponding gauge fields: photons, weak bosons, gluons, Higgs's scalars and the gravitons, which not only explain all the assumptions of the {\it standard model}, and makes several predictions, but also explains the existence of the graviton gauge fields. Analysing the properties of fermion and boson fields concerning how they manifest in $d=(3+1)$, assuming space in $d=(3+1)$ flat, while all the fields have non-zero momenta only in $d=(3+1)$, this article illustrates that scattering of fermion and boson fields, with gravitons included, represented by the Feynman diagrams, are determined by the algebraic products of the corresponding ``basis vectors'' of fields, contributing to scattering. There are two kinds of boson gauge fields appearing in this theory, both contribute when describing scattering. We illustrate, assuming that the internal space, which manifests in $d=(3+1)$ origin in $d=(5+1)$, and in $d=(13+1)$, the annihilation of an electron and positron into two photons, and the scattering of an electron and positron into two muons. The theory offers an elegant and promising illustration of the interaction among fermion and boson second quantised fields.