A Rigorous Mathematical Proof of the Yang-Mills Mass Gap via Fractal Corrections
Year: 2025
Type: article
Abstract: One of the Millennium Prize Problems in mathematical physics is the proof of the massgap in non-Abelian Yang-Mills theory. This paper presents a rigorous proof that the lowesteigenvalue of the Yang-Mills Hamiltonian remains strictly positive, ensuring the existence ofa nonzero mass gap. Our proof introduces a novel fractal correction function, which stabilizesthe spectral structure of the gauge field operator. Using spectral analysis, the Rayleigh-Ritzmethod, and Schwinger-Dyson equations, we establish a strict lower bound on the mass gap.This work provides a fundamental mathematical solution to the non-perturbative problemof quantum gauge fields.
Author: Leclerc, Dominic
Language: English
Subfield: Nuclear and High Energy Physics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W6969019874
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