Do we understand the internal spaces of second quantized fermion and boson fields, with gravity included? Relation with strings theories (2312.07548v2)

Abstract: The article proposes the description of internal spaces of fermion (quarks and leptons and antiquarks and antileptons) and boson (photons, weak bosons, gluons, gravitons and scalars) second quantized fields in a unique way if they all are massless. The internal spaces are described by ``basis vectors'', which are the superposition of odd (for fermions) and even (for bosons) products of the operators $\gamma^ {a}$. For an arbitrary symmetry $SO(d-1,1)$ of the internal spaces, it is the number of fermion fields (they appear in families and have their Hermitian conjugated partners in a separate group) equal to the number of boson fields (they appear in two orthogonal groups), manifesting a kind of supersymmetry, which differ of the string supersymmetry. On the assumption that fermions and bosons are active (they have momenta different from zero) only in $d=(3+1)$ ordinary space-time, bosons present vectors if they carry the space index $\mu=(0,1,2,3)$, and present scalars if they carry the index $\sigma \ge 5$. The author discusses this theory's latest achievements, with a trial to understand whether the extension to strings or to odd-dimensional spaces can lead to a new kind of supersymmetry. This model, named {\it spin-charge-family} theory, manifests in a long series of papers on the phenomenological success of the theory in elementary particle physics and cosmology.