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 superpositions of odd and even products of the operators γa, with the index a running in internal and external space-time, suggests in d=2(2n+1)-dimensions in internal space, such as d=(13+1), and d=(3+1) in external space-time, a unified picture of all so far observed fermions and bosons. Quarks, leptons, antiquarks, and antileptons appear in families - each family contains fermions and antifermions. Bosons—gravitons, photons, weak bosons, gluons, and scalars, which carry the spatial index α (for tensors and vectors α=n=(0,1,2,3) and for scalars α≥5)—appear in two orthogonal groups. All fields are assumed to have non-zero momenta and angular momenta only in the d=(3+1), SO(3,1), of ordinary space-time. 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 bosons. 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 with this theory.