Do we understand the internal spaces of second quantized fermion and boson fields, with gravity included?

Abstract In this paper, the internal spaces of all fermion and boson second quantized fields, with gravity included, are described by “basis vectors” which are the superposition of odd (for fermions) and even (for bosons) products of the operators γ a . For an arbitrarily chosen symmetry SO ( d − 1, 1) of the internal spaces, it is the number of “basis vectors” of fermion fields (appearing in families) equal to the number of “basis vectors” of boson fields, manifesting a kind of supersymmetry. On the assumption that fermions and bosons are active (they have momenta different from zero) only in d = (3 + 1) ordinary space, bosons present vectors if they carry the index µ = (0, 1, 2, 3), and present scalars if they carry the index σ ≥ 5. The author shows in this paper that all the fermion and boson fields can be treated uniquely if they all started as massless fields, discusses this theory’s latest achievements, with a trial to extend point particles to strings. This model, named spin-charge-family theory, manifests in a long series of papers [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11], the phenomenological success of the theory in elementary particle physics and cosmology.