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Four-Variable Jacobian Conjecture in a Topological Quantum Model of Intersecting Fields
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Summary
This preprint introduces in a visual and conceptual way a model of two intersecting curved fields with a shared nucleus, whose quantized dynamics offer potential cases of the four-variable Jacobian conjecture and a nonlinear Hodge cycle.
The Kummer type geometry of the model suggests a unified framework where abstract mathematical developments like Tomita-Takesaki, Gorenstein, and Dolbeault theories, can be conceptually linked to the Jacobian, Hodge, and Riemann conjectures.
Other mathematical physics topics, like the mass gap problem, reflection positivity, the emergence of imaginary time, or t-duality, are also considered within this context.
The fields model also lies the foundation of a novel deterministic quantum atomic system with a supersymmetric dual nucleus structure of matter and mirror antimatter.
Abstract
This paper presents a topological model involving two intersecting curved fields with varying phases that may represent a case of the Jacobian conjecture for four variables. It also suggests connections with other mathematical topics such as Gorenstein Liaison, Tomita-Takesaki modular theory, the Mass gap problem, Reflection positivity, T-duality in string theory, or Hodge theory, all considered within the dual fields model framework.
The dynamics of the fields model may also represent a quantized Hodge cycle where the algebraic varieties are nonlinearly combined.
The mathematical investigation presented in this paper stems from the search for a deterministic atomic model, where two curved fields intersect to create a shared nucleus of matter and its mirror image. This speculative nuclear model is generally described in the paper's concluding section.
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References
De miguel Bueno Alfonso. Four-Variable Jacobian Conjecture in a Topological Quantum Model of Intersecting Fields. 2024. Zenodo. [Cross Ref]