The Topological Redundancy of Scattering Amplitudes and the Graviton
Description
Modern Quantum Field Theory (QFT) describes particle interactions through scattering amplitudes derived from perturbative expansions of gauge theories. While highly successful, these calculations often involve large intermediate expressions with substantial gauge redundancy. Recent developments, including geometric reformulations such as the amplituhedron, suggest that scattering amplitudes may admit simpler underlying structures.
The present work explores whether scattering processes can be interpreted geometrically within the Geometric Monism (GM) framework. In GM, particles are modeled as torsional standing-wave structures in a 5-dimensional manifold governed by the Planck Stiffness \(\kT=c^4/G\), and interactions are modeled as localized topological junctions.
Within this interpretation, helicity configurations and certain constrained scattering processes are described as geometric combinations of torsional axes rather than sums over large perturbative expansions. The analysis suggests that aspects of gauge redundancy may reflect the projection of continuous geometric structure into perturbative formalisms. Additionally, gravity is interpreted as macroscopic elastic strain of the manifold, motivating a geometric perspective complementary to particle-exchange models. These results are presented as interpretive and conceptual, not as replacements for the Standard Model or QFT.
Series information
v2 introduces significant theoretical refinements and terminology updates. The title and text have been streamlined, removing series numeration for broader accessibility and carefully tempering absolute claims to focus on mathematical simplicity rather than definitive proof. Gluons are described as as 'torsional knots' rather than abstract defects. A new subsection has been added to mechanically redefine locality—distinguishing the strictly local nature of wave intersections from the partially non-local 5D depth of the entities themselves—and to explain unitarity as the natural consequence of finite wave phase alignments. Finally, the macroscopic source of gravity has been clarified as the summed dimensional stress of countless individual knot entities, and all references have been perfectly synchronized with the framework's latest foundational papers on QFT wave dynamics.
Series information
Version 3 substantially revises the conceptual framing and presentation of the Geometric Monism (GM) interpretation of scattering processes. Strong claims of replacing quantum field theory (QFT) scattering amplitudes have been removed and replaced with a more precise interpretation of amplitudes as computational representations of underlying geometric topological junctions. The previous reliance on AI-based examples and informal terminology has been replaced with a formal, reviewer-safe comparison of representational complexity. The treatment of helicity, collinear limits, and topological conservation has been retained but reframed as an interpretive geometric model rather than a derivation. The discussion of the graviton has been clarified and strengthened through explicit falsification criteria, and language throughout has been aligned with the broader GM series to ensure consistency and avoid ontological overstatement.
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Topological_Structure_of_Scattering v3.pdf
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