What question did this study set out to answer?

This work aims to develop a robust framework for infrared stabilization in lattice Yang–Mills theory using active spectral coercivity.

May 10, 2026Open Access

Active Spectral Coercivity in Lattice Yang–Mills Theory

Key Points

This work aims to develop a robust framework for infrared stabilization in lattice Yang–Mills theory using active spectral coercivity.
Introduced a modified stochastic quantization framework with spectral gap analysis.
Utilized Bakry–Émery coercivity and Combes–Thomas localization estimates.
Conducted numerical investigations and finite-size scaling studies on autocorrelation suppression.
Demonstrated strong numerical evidence for infrared mass-gap behavior in finite lattices.
Showed effective stochastic stabilization through the proposed framework.

Abstract

This repository contains Version 7 of the Zsa-G framework research program on infrared stabilization in lattice Yang–Mills theory. The work introduces a modified stochastic quantization framework based on active spectral coercivity and localized infrared stabilization. The framework combines finite-lattice spectral gap analysis, Bakry–Émery coercivity methods, Combes–Thomas localization estimates, finite-size scaling studies, and numerical investigations of autocorrelation suppression in stabilized Langevin dynamics. The repository contains: • Main research paper:“Active Spectral Coercivity in Lattice Yang–Mills Theory” • Supplementary Technical Notes:Detailed numerical setup, finite-size scaling methodology, autocorrelation extraction procedures, uncertainty discussion, and localization analysis. • Mathematical Notes:Additional mathematical formulations concerning Bakry–Émery coercivity, Combes–Thomas localization, Dirichlet forms, and invariant-measure preservation. This release extends and consolidates the previous Version 6 research program available within the same DOI version history. The framework does not claim a complete constructive continuum proof of the Yang–Mills Millennium Problem. Instead, it proposes a mathematically structured coercive stochastic stabilization framework with strong numerical evidence for infrared mass-gap behavior on finite lattices.Keywords:Yang–Mills theory, lattice gauge theory, stochastic quantization, Bakry–Émery, Combes–Thomas localization, spectral coercivity, infrared stabilization, Gribov problem, lattice QCD, mathematical physics. Code Availability:The current implementation of the Zsa-G framework remains under active development and is not publicly released at this stage. Representative methodologies and mathematical formulations are provided for scientific transparency. Extended implementation details may be made available in future releases or collaborative settings. Commercial Use Notice:Commercial, industrial, or proprietary implementation of the Zsa-G Framework requires prior written permission from the author.

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