preprints_ui: hnw5p_v1
Data license: ODbL (database) & original licenses (content) · Data source: Open Science Framework
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| hnw5p_v1 | A Constructive Solution to the Clay Millennium Yang–Mills Problem with a Mass Gap in Four Dimensions | We present a constructive framework for a four-dimensional Yang–Mills quantum field theory with compact nonabelian gauge group SU(N), aiming to fulfill the Jaffe–Witten criteria of the Yang–Mills Millennium Problem. The approach proceeds through seven rigorously structured steps: lattice regularization, ultraviolet control, continuum limit, Lorentzian reconstruction, and derivation of a universal, strictly positive mass gap. Building on methods from Balaban’s renormalization group, cluster expansions, and infrared bounds à la Aizenman–Fröhlich–Spencer, the construction satisfies the Osterwalder–Schrader, Wightman, and Haag–Kastler axioms. While some technical results are assumed from prior literature (e.g., RG multiscale bounds), all steps are logically explicit and fully cross-referenced. This work offers a concrete candidate for solving the first Clay Millennium Problem from a mathematically constructive standpoint. | 2025-05-09T14:42:09.913766 | 2025-05-09T16:58:01.748866 | 2025-05-09T16:57:47.525242 | osf | 1 | accepted | 1 | 1 | https://doi.org/10.31219/osf.io/hnw5p_v1 | No license | Axiomatic QFT; Cluster Expansion; Constructive Quantum Field Theory; Functional Integration; Gauge Invariance; Glueball Spectrum; Haag–Kastler Framework; Infrared Bounds; Lattice Gauge Theory; Mass Gap; Mathematical Physics; Millennium Prize Problems; Nonperturbative Methods; Osterwalder–Schrader Axioms; Quantum Field Theory; Reflection Positivity; Renormalization Group; SU(N) Gauge Theory; Wightman Axioms; Yang–Mills Theory | ["Axiomatic QFT", "Cluster Expansion", "Constructive Quantum Field Theory", "Functional Integration", "Gauge Invariance", "Glueball Spectrum", "Haag\u2013Kastler Framework", "Infrared Bounds", "Lattice Gauge Theory", "Mass Gap", "Mathematical Physics", "Millennium Prize Problems", "Nonperturbative Methods", "Osterwalder\u2013Schrader Axioms", "Quantum Field Theory", "Reflection Positivity", "Renormalization Group", "SU(N) Gauge Theory", "Wightman Axioms", "Yang\u2013Mills Theory"] | David Gutierrez Ule | [{"id": "s2cz4", "name": "David Gutierrez Ule", "index": 0, "orcid": null, "bibliographic": true}] | David Gutierrez Ule | Physical Sciences and Mathematics | [{"id": "584240d954be81056ceca9a1", "text": "Physical Sciences and Mathematics"}] | https://osf.io/download/681e144c45b3be4306700255 | 0 | not_applicable | not_applicable | [] | 2025-05-10T00:11:34.207827 |