How do Clifford algebras show the way to the second quantized fermions with unified spins, charges and families, and to the corresponding second quantized vector and scalar gauge fields

Abstract

This contribution presents properties of the second quantized not only fermion fields but also boson fields, if the second quantization of both kinds of fields origins in the description of the internal space of fields with the ''basis vectors'' which are the superposition of odd (when describing fermions) or even (when describing bosons) products of the Clifford algebra operators $\gamma^a$'s. The tensor products of the ''basis vectors'' with the basis in ordinary space forming the creation operators manifest the anticommutativty (of fermions) or commutativity (of bosons) of the ''basis vectors'', explaining the second quantization postulates of both kinds of fields. Creation operators of boson fields have all the properties of the gauge fields of the corresponding fermion fields, offering a new understanding of the fermion and boson fields.