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Other literature type . 2026
License: CC BY
Data sources: ZENODO
ZENODO
Other literature type . 2026
License: CC BY
Data sources: Datacite
ZENODO
Other literature type . 2026
License: CC BY
Data sources: Datacite
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Spectral Vacuum Mechanism – Part XVII Spectral Confinement under Truncated SU(3) Gauge Embedding: Toward a Constructive QCD-Motivated Lattice Framework

Authors: Nemirovsky, Mikhail;

Spectral Vacuum Mechanism – Part XVII Spectral Confinement under Truncated SU(3) Gauge Embedding: Toward a Constructive QCD-Motivated Lattice Framework

Abstract

ABSTRACT This work develops the next stage of the Spectral Vacuum Mechanism (SVM), extending the constructive spectral-confinement framework from a truncated SU(2) gauge embedding (Part XVI) to the non-Abelian SU(3) gauge group, which is fundamental to Quantum Chromodynamics (QCD). We construct a finite-dimensional, truncated SU(3) gauge–matter Hamiltonian on a d-dimensional cubic lattice, incorporating matter fields, truncated link variables, and plaquette interactions. All local Hilbert spaces are kept finite-dimensional, and all interaction operators are uniformly bounded, enabling a fully constructive spectral analysis. The central result of this study is the derivation of an explicit, dimension-dependent lower bound on the spectral gap Delta: Delta >= m0 - 2 z(d) ( g Vmax + kappa Vmax ) - C_box(d) lambda Wmax We introduce a group-dependent scaling factor g_G, revealing that the SU(3) interaction density introduces a "penalty" twice as large as the SU(2) case (g_SU(3) = 2 vs g_SU(2) = 1). This results in a more aggressive "magnetic stiffness" of the vacuum as the lattice dimensionality d increases. Our analysis provides two major physical predictions: Dimensional Stability: The vacuum remains stable and gapped for d = 3 and d = 4, but the gap bound formally vanishes for d >= 5, suggesting that four-dimensional spacetime represents the upper stability limit for this confinement mechanism. Scaling Laws: We predict a specific correlation-length ratio between dimensions, R43 = xi_4 / xi_3 approx 1.41 +/- 0.15, and a corresponding increase in the string-tension scaling factor sigma_4 / sigma_3 approx 2.0. These results demonstrate that the SVM framework remains robust under the complexity of SU(3) color symmetry, providing a rigorous path toward a constructive proof of the mass gap in QCD-motivated models. Keywords Spectral Vacuum Mechanism • SU(3) gauge theory • spectral confinement • mass gap • truncated gauge embedding • plaquette dynamics • constructive quantum field theory • lattice Hamiltonians • Block‑EGC • spectral gap bounds • confinement mechanism • correlation length • string tension • non‑Abelian gauge structure • QCD‑like models

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selected citations
These citations are derived from selected sources.
This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Citations provided by BIP!
popularity
This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
BIP!Popularity provided by BIP!
influence
This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Influence provided by BIP!
impulse
This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
BIP!Impulse provided by BIP!
0
Average
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