Internal spaces of fermion and boson fields, described with the superposition of odd and even products of $γ^{a}$, enable understanding of all the second-quantised fields in an equivalent way

Abstract

Using the odd and even ``basis vectors'', which are the superposition of odd and even products of $γ^a$'s, to describe the internal spaces of the second quantised fermion and boson fields, respectively, offers in even-dimensional spaces, like it is $d=(13+1)$, the unique description of all the properties of the observed fermion fields (quarks and leptons and antiquarks and antileptons appearing in families) and boson fields (gravitons, photons, weak bosons, gluons and scalars) in a unique way, providing that all the fields have non zero momenta only in $d =(3+1)$ of the ordinary space-time, bosons have the space index $α$ (which is for tensors and vectors $μ=(0,1,2,3)$ and for scalars $σ\ge 5$). In any even-dimensional space, there is the same number of internal states of fermions appearing in families and their Hermitian conjugate partners as it is of the two orthogonal groups of boson fields having the Hermitian conjugate partners within the same group. A simple action for massless fermion and boson fields describes all the fields uniquely. The paper overviews the theory, presents new achievements and discusses the open problems of this theory.