Algebraic Localization of Spin-3/2 Fields and Geometric Cutoff of Fundamental Fields via Higher-Order Octonionic Forms

In modern quantum field theory and superstring theory, the existence of a finite number of massless high-spin fields is severely constrained by no-go theorems, most notably the Weinberg-Witten theorem. In this study, based on the degree of polynomial forms of octonions, which constitute the highest-dimensional normed division algebra over the reals, we demonstrate the inevitability of a finite cutoff for massless high-spin fields as an algebraic self-collapse of the causal propagator. We formulate the fundamental fields of the universe as a polynomial structure of octonions—the maximal-dimensional composition algebra—and establish a unique correspondence where zeroth-order forms map to mass (scalar fields), first-order forms to matter (spinor fields), and second-order forms to gauge fields and spacetime curvature (vector and tensor fields). Furthermore, we derive an algebraic localization description of spin-3/2 fields (gravitinos) from third-order forms originating from the nonassociativity inherent in octonions. To circumvent the violation of quantum unitarity induced by nonassociativity, we introduce an approach that formulates these higher-order forms as geometric waveforms at the classical stage prior to second quantization. Finally, we prove that algebraic extensions beyond fourth-order forms lose the multiplicity of the norm due to constraints imposed by Hurwitz’s theorem, thereby generating a maximal ideal domain of algebraic zero-divisors on the Cayley-Dickson construction. By constructing an explicit mapping from the appearance of these zero divisors to the non-local collapse of the causal propagator, we elucidate the geometric and algebraic necessity that massless high-spin fields cannot exist infinitely and must undergo a finite cutoff at the spin-3/2 or spin-2 stage.