Clifford odd and even objects in even and odd dimensional spaces describing internal spaces of fermion and boson fields

Abstract

In a long series of works, it has been demonstrated, that the {\it spin-charge-family} theory offers the explanation for all in the {\it standard model} assumed properties of the second quantized fermion and boson fields, offering several predictions as well as explanations for several of the observed phenomena. The theory assumes a simple starting action in even dimensional spaces with $d \ge (13 +1)$ with massless fermions interacting with gravity only. The internal spaces of fermion and boson fields are described by the Clifford odd and even objects, respectively. This contribution discusses the properties of the fermion and boson fields in odd dimensional spaces, $d=(2n +1)$, with the internal spaces of fermion and boson fields described again by the Clifford odd and even objects, respectively, pointing out that their properties differ essentially from the properties in even dimensional spaces, resembling the ghost needed when looking for final solutions with Feynman diagrams.