aiqbench analysis
This paper advances fundamental quantum mechanics by applying connection factorization techniques to constrained motion on geometric manifolds like curves and surfaces. It derives exact half-connection decompositions for Laplace operators and analyzes Dirac reductions, revealing hidden nilpotent covariant differential complexes within these structures. The work represents a significant theoretical contribution to the mathematical foundations of quantum physics rather than an application of current AI or machine learning systems.
Connection Factorization in Constrained Quantum Mechanics
arXiv:2605.29241v2 Announce Type: replace-cross Abstract: We investigate constrained quantum motion on curves and surfaces using connection factorization methods. We show that Laplace operators admit an exact half-connection factorization generated by connection one-forms. The first-order part of the Laplacian is identified with the Darboux rotational connection of the orthogonal frame. Elimination of this rotational connection naturally produces quadratic geometric invariants analogous to supersymmetric Riccati potentials. Using orthonormal moving frames, we derive effective geometric contributions for planar curves, spatial curves, and embedded surfaces. We further analyze Dirac reductions using structure equations and show that for Fermi-type reductions the scalar Jensen--Koppe--da Costa contribution is cancelled in the reduced Dirac sector, leaving a residual first-order spinorial derivative structure. The resulting framework suggests the existence of hidden nilpotent covariant differential complexes naturally generated by geometric connection structures.
Abstract:We investigate constrained quantum motion on curves and surfaces using connection factorization methods. We show that Laplace operators admit an exact half-connection factorization generated by connection one-forms. The first-order part of the Laplacian is identified with the Darboux rotational connection of the orthogonal frame. Elimination of this rotational connection naturally produces quadratic geometric invariants analogous to supersymmetric Riccati potentials. Using orthonormal moving frames, we derive effective geometric contributions for planar curves, spatial curves, and embedded surfaces. We further analyze Dirac reductions using structure equations and show that for Fermi-type reductions the scalar Jensen--Koppe--da Costa contribution is cancelled in the reduced Dirac sector, leaving a residual first-order spinorial derivative structure. The resulting framework suggests the existence of hidden nilpotent covariant differential complexes naturally generated by geometric connection structures.
14 pages. Corrected author name
arXiv:2605.29241 [math-ph]
(or arXiv:2605.29241v2 [math-ph] for this version)
https://doi.org/10.48550/arXiv.2605.29241 Focus to learn more arXiv-issued DOI via DataCite
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Full text under the publisher's open licence · 221 words
