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Validity of two bosonic gauge-field types (A^I and A^II)

Ascertain whether the two kinds of boson fields A^{I}_{f} and A^{II}_{f} introduced to represent vector and scalar gauge fields within the spin–charge–family theory provide the correct and complete description of bosonic fields, including consistency with their interpretation in the Feynman-diagrammatic analysis.

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Background

The framework posits two distinct families of even bosonic basis vectors: A{I}_{f}, which mediate transformations among members within the same family, and A{II}_{f}, which mediate transformations of the same member across different families.

These two classes are positioned as replacements for the two kinds of gauge connections ω{abα} and ˜ω{abα} used in prior formulations. The authors explicitly question whether this split yields the correct physical description.

References

There remain questions to be answered: iv.b. Do two kinds of boson fields, A I ˆm† and IIA , appearing in this theory (offering the interpretation of the Feynman diagrams and elegantly confirming the requirement of the two kinds of fields, ω and ω˜ , appearing in Eq. (70) and used so far in the spin-charge-family theory ([8] and references therein)) offer the correct (true) description of the boson fields?

— Can the "basis vectors", describing the internal spaces of fermion and boson fields with the Clifford odd (for fermion) and Clifford even (for boson) objects, explain interactions among fields, with gravitons included? (2407.09482 - Borštnik, 10 May 2024) in Section 4 (Conclusions), iv.b