A new way to unify all fermion and boson fields, including gravity

Abstract

The description of the internal spaces of fermion and boson fields with "basis vectors", which are the superposition of odd and even products of the operators $\gamma^a$, offers in $d=2(2n+1)$-dimensions, such as $d=(13+1)$, a unified picture of all so far observed fermions (quarks, leptons, antiquarks and antileptons that appear in families) and bosons (gravitons, photons, weak bosons, gluons and scalars), under the condition that all fields have non-zero angular momenta only in the $d =(3+1)$, $SO(3,1)$, of ordinary space-time. Bosons, which also carry the spatial index $\alpha$ (which is for tensors and vectors $\mu =(0,1,2,3)$ and for scalars $\sigma \ge 5$) appear in two orthogonal groups. In any $d=2(2n+1)$-dimensional space the number of internal states of fermions in all families and their Hermitian conjugate partners is equal to the number of internal states of boson states. The article presents general properties of massless fermion and boson fields and their mutual interactions in this theory, which determine the Lagrangian density of both fields and their interactions. It particularly illustrates "basis vectors" and their properties in $d=(13+1)$ and $d=(5+1)$. The article presents new results and discusses open problems in this theory.