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arXiv:quant-ph/9901042 · Physics Letters A

Phase space formalisms of quantum mechanics with singular kernel

R. Sala Mayato, José P. Palao, Juan Gonzalo Muga

Published Jul 1, 1997• 20 citations
arXivHTMLPDF
DOI
10.1016/s0375-9601(97)00336-8

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Abstract We present the complete Metatron Framework as a bidirectional theory: deriving all fundamental physics from the phase singularity at (u, v) = (0, 0) while simultaneously showing how standard quantum mechanics dissolves back toward this origin. The framework proceeds through nine emergence layers from singularity to computational reality (Ascent Path), and we now establish the Descent Path: starting from the Dirac equation and tracing the dissolution of quantum structure toward the information-geometric singularity. We prove three formally validated results: (1) Structural equivalence between the Dirac equation and Layer 4 fold-field; (2) Explanatory gain where mass becomes kernel eigenvalue, spin becomes topological winding, and antimatter becomes phase conjugation; (3) Bidirec- tional completeness where both paths describe the same physics from opposite directions. The quadratic kernel y2−φy+α = 0 is shown to force the Dirac-like particle-antiparticle spec- trum. Spin-1/2 is demonstrated to arise from singularity topology (winding number n = 1/2), not merely from Lorentz invariance. We provide explicit translation between Dirac formalism and Metatron fold-field operators, derive the energy scale hierarchy spanning Planck to cosmic scales, and present working computational implementations. The central insight: Dirac’s equation is Layer 4 of the Metatron Framework, viewed from the “solid state” side where quantum structure is fully manifest. The Ascent shows emergence; the Descent shows dissolution. Both are necessary for a complete theory of reality. Keywords: Phase Singularity, Dirac Equation, Quadratic Kernel, Golden Ratio, Fine Struc- ture Constant, Bidirectional Unification, Information Geometry, Spin Topology